[{"status":"public","ddc":["500"],"OA_type":"hybrid","type":"journal_article","title":"Off-diagonal Ramsey numbers for linear hypergraphs","publication_status":"epub_ahead","fulldoi":"https://doi.org/10.1017/s0963548326100443","arxiv":1,"oa":1,"article_processing_charge":"No","mathsc":["05D10","05D40","05C65"],"page":"1-14","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"language":[{"iso":"eng"}],"OA_place":"publisher","author":[{"full_name":"He, Xiaoyu","first_name":"Xiaoyu","last_name":"He"},{"first_name":"Jiaxi","last_name":"Nie","full_name":"Nie, Jiaxi"},{"full_name":"Wigderson, Yuval","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","last_name":"Wigderson"},{"full_name":"Yu, Hung-Hsun","first_name":"Hung-Hsun","last_name":"Yu"}],"date_updated":"2026-07-08T07:24:54Z","date_created":"2026-06-29T10:47:02Z","year":"2026","citation":{"mla":"He, Xiaoyu, et al. “Off-Diagonal Ramsey Numbers for Linear Hypergraphs.” <i>Combinatorics, Probability and Computing</i>, Cambridge University Press, 2026, pp. 1–14, doi:<a href=\"https://doi.org/10.1017/s0963548326100443\">10.1017/s0963548326100443</a>.","short":"X. He, J. Nie, Y. Wigderson, H.-H. Yu, Combinatorics, Probability and Computing (2026) 1–14.","ieee":"X. He, J. Nie, Y. Wigderson, and H.-H. Yu, “Off-diagonal Ramsey numbers for linear hypergraphs,” <i>Combinatorics, Probability and Computing</i>. Cambridge University Press, pp. 1–14, 2026.","chicago":"He, Xiaoyu, Jiaxi Nie, Yuval Wigderson, and Hung-Hsun Yu. “Off-Diagonal Ramsey Numbers for Linear Hypergraphs.” <i>Combinatorics, Probability and Computing</i>. Cambridge University Press, 2026. <a href=\"https://doi.org/10.1017/s0963548326100443\">https://doi.org/10.1017/s0963548326100443</a>.","apa":"He, X., Nie, J., Wigderson, Y., &#38; Yu, H.-H. (2026). Off-diagonal Ramsey numbers for linear hypergraphs. <i>Combinatorics, Probability and Computing</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0963548326100443\">https://doi.org/10.1017/s0963548326100443</a>","ama":"He X, Nie J, Wigderson Y, Yu H-H. Off-diagonal Ramsey numbers for linear hypergraphs. <i>Combinatorics, Probability and Computing</i>. 2026:1-14. doi:<a href=\"https://doi.org/10.1017/s0963548326100443\">10.1017/s0963548326100443</a>","ista":"He X, Nie J, Wigderson Y, Yu H-H. 2026. Off-diagonal Ramsey numbers for linear hypergraphs. Combinatorics, Probability and Computing., 1–14."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/S0963548326100443"}],"publication":"Combinatorics, Probability and Computing","scopus_import":"1","abstract":[{"lang":"eng","text":"We study off-diagonal Ramsey numbers 𝑟⁡(𝐻,𝐾(𝑘)\r\n𝑛) of 𝑘-uniform hypergraphs, where 𝐻 is a fixed linear 𝑘-uniform hypergraph and 𝐾(𝑘)\r\n𝑛 is complete on 𝑛 vertices. Recently, Conlon, Fox, Gunby, He, Mubayi, Suk, and Verstraëte disproved the folklore conjecture that 𝑟⁡(𝐻,𝐾(3)\r\n𝑛) always grows polynomially in 𝑛. In this paper, we show that much larger growth rates are possible in higher uniformity. In uniformity 𝑘 ≥4, we prove that for any constant 𝐶 >0, there exists a linear 𝑘-uniform hypergraph 𝐻 for which\r\n\r\n𝑟⁡(𝐻,𝐾(𝑘)\r\n𝑛)≥twr𝑘−2⁢(2(log⁡𝑛)𝐶)."}],"doi":"10.1017/s0963548326100443","day":"14","date_published":"2026-04-14T00:00:00Z","oa_version":"Published Version","month":"04","publisher":"Cambridge University Press","external_id":{"arxiv":["2507.05641"]},"_id":"22152","quality_controlled":"1","extern":"1","article_type":"original","publication_identifier":{"eissn":["1469-2163"],"issn":["0963-5483"]}},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"85-138","language":[{"iso":"eng"}],"mathsc":["05D10","05C55"],"article_processing_charge":"No","oa":1,"OA_place":"repository","OA_type":"green","type":"journal_article","status":"public","fulldoi":"https://doi.org/10.24033/ast.1255","arxiv":1,"title":"Exposé Bourbaki 1230 : Upper bounds on diagonal Ramsey numbers (after Campos, Griffiths, Morris, and Sahasrabudhe)","publication_status":"published","_id":"22184","external_id":{"arxiv":["2411.09321"]},"oa_version":"Preprint","month":"01","publisher":"Societe Mathematique de France","publication_identifier":{"issn":["0303-1179","2492-5926"]},"article_type":"original","extern":"1","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2411.09321 "}],"publication":"Astérisque","year":"2026","date_created":"2026-06-29T12:02:59Z","citation":{"chicago":"Wigderson, Yuval. “Exposé Bourbaki 1230 : Upper Bounds on Diagonal Ramsey Numbers (after Campos, Griffiths, Morris, and Sahasrabudhe).” <i>Astérisque</i>. Societe Mathematique de France, 2026. <a href=\"https://doi.org/10.24033/ast.1255\">https://doi.org/10.24033/ast.1255</a>.","mla":"Wigderson, Yuval. “Exposé Bourbaki 1230 : Upper Bounds on Diagonal Ramsey Numbers (after Campos, Griffiths, Morris, and Sahasrabudhe).” <i>Astérisque</i>, Societe Mathematique de France, 2026, pp. 85–138, doi:<a href=\"https://doi.org/10.24033/ast.1255\">10.24033/ast.1255</a>.","ieee":"Y. Wigderson, “Exposé Bourbaki 1230 : Upper bounds on diagonal Ramsey numbers (after Campos, Griffiths, Morris, and Sahasrabudhe),” <i>Astérisque</i>. Societe Mathematique de France, pp. 85–138, 2026.","short":"Y. Wigderson, Astérisque (2026) 85–138.","ista":"Wigderson Y. 2026. Exposé Bourbaki 1230 : Upper bounds on diagonal Ramsey numbers (after Campos, Griffiths, Morris, and Sahasrabudhe). Astérisque., 85–138.","ama":"Wigderson Y. Exposé Bourbaki 1230 : Upper bounds on diagonal Ramsey numbers (after Campos, Griffiths, Morris, and Sahasrabudhe). <i>Astérisque</i>. 2026:85-138. doi:<a href=\"https://doi.org/10.24033/ast.1255\">10.24033/ast.1255</a>","apa":"Wigderson, Y. (2026). Exposé Bourbaki 1230 : Upper bounds on diagonal Ramsey numbers (after Campos, Griffiths, Morris, and Sahasrabudhe). <i>Astérisque</i>. Societe Mathematique de France. <a href=\"https://doi.org/10.24033/ast.1255\">https://doi.org/10.24033/ast.1255</a>"},"date_updated":"2026-07-14T09:53:07Z","author":[{"id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","first_name":"Yuval","last_name":"Wigderson","full_name":"Wigderson, Yuval"}],"doi":"10.24033/ast.1255","date_published":"2026-01-01T00:00:00Z","day":"01","scopus_import":"1","abstract":[{"lang":"eng","text":"Ramsey's theorem states that if N\r\n is sufficiently large, then no matter how one colors the edges among N\r\n vertices with two colors, there are always k\r\n vertices spanning edges in only one color. Given this theorem, it is natural to ask \"how large is sufficiently large?\" Ramsey's original proof showed that N=k!\r\n is sufficient, and five years later Erdős and Szekeres improved this bound to N=4^k\r\n. And then progress stalled for almost 90 years.\r\n\r\nIn this survey, I present the history of the problem, and discuss some of the ideas used in the recent breakthrough of Campos–Griffiths–Morris–Sahasrabudhe, who proved that N=3.993^k\r\n is sufficient. In addition, I discuss the subsequent work of Balister, Bollobás, Campos, Griffiths, Hurley, Morris, Sahasrabudhe, and Tiba, who gave an alternative, and more conceptual, proof."},{"text":"Le théorème de Ramsey stipule que si N\r\n est suffisamment grand, alors quelle que soit la manière dont l'on colore les arêtes entre N\r\n sommets avec deux couleurs, il y a toujours k\r\n sommets dont les arêtes ne sont colorées que d'une seule couleur. Compte tenu de ce théorème, il est naturel de se demander \"À quel point N\r\n doit être grand ?\" La preuve originale de Ramsey a montré que N=k!\r\n suffit, et cinq ans plus tard, Erdős et Szekeres ont amélioré cette borne à N=4k\r\n. Puis le progrès s'est arrêté pendant près de 90 ans.\r\n\r\nDans cet exposé, je présente l'histoire du problème et je discute certaines idées utilisées dans la percée récente de Campos--Griffiths-Morris--Sahasrabudhe, qui ont prouvé que N=3,993k\r\n suffit. De plus, je discute le travail suivant de Balister, Bollobás, Campos, Griffiths, Hurley, Morris, Sahasrabudhe, et Tiba, qui ont donné une preuve alternative et plus conceptuelle.","lang":"fre"}]},{"quality_controlled":"1","issue":"3","extern":"1","intvolume":"        39","publication_identifier":{"eissn":["1095-7146"],"issn":["0895-4801"]},"article_type":"original","volume":39,"publisher":"Society for Industrial & Applied Mathematics","oa_version":"Preprint","month":"09","external_id":{"arxiv":["2410.08644"]},"_id":"22155","scopus_import":"1","abstract":[{"text":"The canonical Ramsey theorem of Erdős and Rado implies that for any graph 𝐻, any edge-coloring (with an arbitrary number of colors) of a sufficiently large complete graph 𝐾𝑁 contains a monochromatic, lexicographic, or rainbow copy of 𝐻. The least such 𝑁 is called the Erdős–Rado number of 𝐻, denoted by 𝐸⁢𝑅⁡(𝐻). Erdős–Rado numbers of cliques have received considerable attention, and in this paper we extend this line of research by studying Erdős–Rado numbers of sparse graphs. For example, we prove that if 𝐻 has bounded degree, then 𝐸⁢𝑅⁡(𝐻) is polynomial in |𝑉⁡(𝐻)| if 𝐻 is bipartite but exponential in general. We also study the closely related problem of constrained Ramsey numbers. For a given tree S and given path 𝑃𝑡, we study the minimum 𝑁 such that every edge-coloring of 𝐾𝑁 contains a monochromatic copy of S or a rainbow copy of 𝑃𝑡. We prove a nearly optimal upper bound for this problem, which differs from the best known lower bound by a function of inverse Ackermann type.","lang":"eng"}],"day":"01","date_published":"2025-09-01T00:00:00Z","doi":"10.1137/24m1714964","author":[{"last_name":"Gishboliner","first_name":"Lior","full_name":"Gishboliner, Lior"},{"full_name":"Milojević, Aleksa","last_name":"Milojević","first_name":"Aleksa"},{"full_name":"Sudakov, Benny","first_name":"Benny","last_name":"Sudakov"},{"id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","first_name":"Yuval","last_name":"Wigderson","full_name":"Wigderson, Yuval"}],"date_updated":"2026-07-08T07:38:44Z","citation":{"ieee":"L. Gishboliner, A. Milojević, B. Sudakov, and Y. Wigderson, “Canonical Ramsey numbers of sparse graphs,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 39, no. 3. Society for Industrial &#38; Applied Mathematics, pp. 1491–1519, 2025.","short":"L. Gishboliner, A. Milojević, B. Sudakov, Y. Wigderson, SIAM Journal on Discrete Mathematics 39 (2025) 1491–1519.","mla":"Gishboliner, Lior, et al. “Canonical Ramsey Numbers of Sparse Graphs.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 39, no. 3, Society for Industrial &#38; Applied Mathematics, 2025, pp. 1491–519, doi:<a href=\"https://doi.org/10.1137/24m1714964\">10.1137/24m1714964</a>.","chicago":"Gishboliner, Lior, Aleksa Milojević, Benny Sudakov, and Yuval Wigderson. “Canonical Ramsey Numbers of Sparse Graphs.” <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial &#38; Applied Mathematics, 2025. <a href=\"https://doi.org/10.1137/24m1714964\">https://doi.org/10.1137/24m1714964</a>.","apa":"Gishboliner, L., Milojević, A., Sudakov, B., &#38; Wigderson, Y. (2025). Canonical Ramsey numbers of sparse graphs. <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/24m1714964\">https://doi.org/10.1137/24m1714964</a>","ama":"Gishboliner L, Milojević A, Sudakov B, Wigderson Y. Canonical Ramsey numbers of sparse graphs. <i>SIAM Journal on Discrete Mathematics</i>. 2025;39(3):1491-1519. doi:<a href=\"https://doi.org/10.1137/24m1714964\">10.1137/24m1714964</a>","ista":"Gishboliner L, Milojević A, Sudakov B, Wigderson Y. 2025. Canonical Ramsey numbers of sparse graphs. SIAM Journal on Discrete Mathematics. 39(3), 1491–1519."},"year":"2025","date_created":"2026-06-29T10:49:48Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.08644","open_access":"1"}],"publication":"SIAM Journal on Discrete Mathematics","OA_place":"repository","oa":1,"article_processing_charge":"No","mathsc":["05D10"],"language":[{"iso":"eng"}],"page":"1491-1519","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","title":"Canonical Ramsey numbers of sparse graphs","arxiv":1,"fulldoi":"https://doi.org/10.1137/24m1714964","status":"public","type":"journal_article","OA_type":"green"},{"OA_place":"repository","oa":1,"mathsc":["05C70","05D10","05C80"],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"language":[{"iso":"eng"}],"title":"Resolution of the Kohayakawa–Kreuter conjecture","publication_status":"published","fulldoi":"https://doi.org/10.1112/plms.70013","arxiv":1,"status":"public","ddc":["500"],"OA_type":"green","type":"journal_article","quality_controlled":"1","extern":"1","article_number":"e70013","issue":"1","intvolume":"       130","volume":130,"publication_identifier":{"eissn":["1460-244X"],"issn":["0024-6115"]},"article_type":"original","oa_version":"Preprint","month":"01","publisher":"Wiley","external_id":{"arxiv":["2402.03045"]},"_id":"22157","abstract":[{"lang":"eng","text":"A graph 𝐺 is said to be Ramsey for a tuple of graphs(𝐻 1 , … , 𝐻𝑟 ) if every 𝑟-coloring of the edges of 𝐺 con-tains a monochromatic copy of 𝐻𝑖 in color 𝑖, for some 𝑖.A fundamental question at the intersection of Ramseytheory and the theory of random graphs is to deter-mine the threshold at which the binomial randomgraph 𝐺𝑛,𝑝 becomes asymptotically almost surely Ram-sey for a fixed tuple (𝐻 1 , … , 𝐻𝑟 ), and a famous conjectureof Kohayakawa and Kreuter predicts this threshold.Earlier work of Mousset–Nenadov–Samotij, Bowtell–Hancock–Hyde, and Kuperwasser–Samotij–Wigdersonhas reduced this probabilistic problem to a determinis-tic graph decomposition conjecture. In this paper, weresolve this deterministic problem, thus proving theKohayakawa–Kreuter conjecture. Along the way, weprove a number of novel graph decomposition resultsthat may be of independent interest."}],"scopus_import":"1","doi":"10.1112/plms.70013","day":"01","date_published":"2025-01-01T00:00:00Z","author":[{"full_name":"Christoph, Micha","first_name":"Micha","last_name":"Christoph"},{"last_name":"Martinsson","first_name":"Anders","full_name":"Martinsson, Anders"},{"last_name":"Steiner","first_name":"Raphael","full_name":"Steiner, Raphael"},{"full_name":"Wigderson, Yuval","last_name":"Wigderson","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5"}],"date_updated":"2026-07-08T10:24:21Z","date_created":"2026-06-29T10:50:35Z","year":"2025","citation":{"ama":"Christoph M, Martinsson A, Steiner R, Wigderson Y. Resolution of the Kohayakawa–Kreuter conjecture. <i>Proceedings of the London Mathematical Society</i>. 2025;130(1). doi:<a href=\"https://doi.org/10.1112/plms.70013\">10.1112/plms.70013</a>","ista":"Christoph M, Martinsson A, Steiner R, Wigderson Y. 2025. Resolution of the Kohayakawa–Kreuter conjecture. Proceedings of the London Mathematical Society. 130(1), e70013.","apa":"Christoph, M., Martinsson, A., Steiner, R., &#38; Wigderson, Y. (2025). Resolution of the Kohayakawa–Kreuter conjecture. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.70013\">https://doi.org/10.1112/plms.70013</a>","chicago":"Christoph, Micha, Anders Martinsson, Raphael Steiner, and Yuval Wigderson. “Resolution of the Kohayakawa–Kreuter Conjecture.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/plms.70013\">https://doi.org/10.1112/plms.70013</a>.","mla":"Christoph, Micha, et al. “Resolution of the Kohayakawa–Kreuter Conjecture.” <i>Proceedings of the London Mathematical Society</i>, vol. 130, no. 1, e70013, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/plms.70013\">10.1112/plms.70013</a>.","short":"M. Christoph, A. Martinsson, R. Steiner, Y. Wigderson, Proceedings of the London Mathematical Society 130 (2025).","ieee":"M. Christoph, A. Martinsson, R. Steiner, and Y. Wigderson, “Resolution of the Kohayakawa–Kreuter conjecture,” <i>Proceedings of the London Mathematical Society</i>, vol. 130, no. 1. Wiley, 2025."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.03045"}],"publication":"Proceedings of the London Mathematical Society"},{"arxiv":1,"fulldoi":"https://doi.org/10.1017/s0305004125000143","publication_status":"published","title":"On the Kohayakawa–Kreuter conjecture","type":"journal_article","OA_type":"green","status":"public","OA_place":"repository","language":[{"iso":"eng"}],"page":"293-320","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","mathsc":["05C80","05C55","05D10"],"article_processing_charge":"No","oa":1,"day":"28","date_published":"2025-04-28T00:00:00Z","doi":"10.1017/s0305004125000143","abstract":[{"text":"Let us say that a graph G is Ramsey for a tuple (H1, ... , Hr) of graphs if every r-colouring\r\nof the edges of G contains a monochromatic copy of Hi in colour i, for some i ∈ [[r]].\r\nA famous conjecture of Kohayakawa and Kreuter, extending seminal work of Rödl and\r\nRucinski, predicts the threshold at which the binomial random graph ´ Gn,p becomes Ramsey\r\nfor (H1, ... , Hr) asymptotically almost surely.\r\nIn this paper, we resolve the Kohayakawa–Kreuter conjecture for almost all tuples of\r\ngraphs. Moreover, we reduce its validity to the truth of a certain deterministic statement,\r\nwhich is a clear necessary condition for the conjecture to hold. All of our results actually hold in greater generality, when one replaces the graphs H1, ... , Hr by finite families\r\nH1, ... , Hr. Additionally, we pose a natural (deterministic) graph-partitioning conjecture,\r\nwhich we believe to be of independent interest, and whose resolution would imply the\r\nKohayakawa–Kreuter conjecture.","lang":"eng"}],"scopus_import":"1","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2307.16611","open_access":"1"}],"citation":{"chicago":"KUPERWASSER, EDEN, WOJCIECH SAMOTIJ, and Yuval Wigderson. “On the Kohayakawa–Kreuter Conjecture.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/s0305004125000143\">https://doi.org/10.1017/s0305004125000143</a>.","ieee":"E. KUPERWASSER, W. SAMOTIJ, and Y. Wigderson, “On the Kohayakawa–Kreuter conjecture,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 178, no. 3. Cambridge University Press, pp. 293–320, 2025.","short":"E. KUPERWASSER, W. SAMOTIJ, Y. Wigderson, Mathematical Proceedings of the Cambridge Philosophical Society 178 (2025) 293–320.","mla":"KUPERWASSER, EDEN, et al. “On the Kohayakawa–Kreuter Conjecture.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 178, no. 3, Cambridge University Press, 2025, pp. 293–320, doi:<a href=\"https://doi.org/10.1017/s0305004125000143\">10.1017/s0305004125000143</a>.","ista":"KUPERWASSER E, SAMOTIJ W, Wigderson Y. 2025. On the Kohayakawa–Kreuter conjecture. Mathematical Proceedings of the Cambridge Philosophical Society. 178(3), 293–320.","ama":"KUPERWASSER E, SAMOTIJ W, Wigderson Y. On the Kohayakawa–Kreuter conjecture. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2025;178(3):293-320. doi:<a href=\"https://doi.org/10.1017/s0305004125000143\">10.1017/s0305004125000143</a>","apa":"KUPERWASSER, E., SAMOTIJ, W., &#38; Wigderson, Y. (2025). On the Kohayakawa–Kreuter conjecture. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0305004125000143\">https://doi.org/10.1017/s0305004125000143</a>"},"date_created":"2026-06-29T10:55:00Z","year":"2025","date_updated":"2026-07-14T08:38:08Z","author":[{"last_name":"KUPERWASSER","first_name":"EDEN","full_name":"KUPERWASSER, EDEN"},{"full_name":"SAMOTIJ, WOJCIECH","first_name":"WOJCIECH","last_name":"SAMOTIJ"},{"first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","last_name":"Wigderson","full_name":"Wigderson, Yuval"}],"publication_identifier":{"eissn":["1469-8064"],"issn":["0305-0041"]},"article_type":"original","volume":178,"intvolume":"       178","extern":"1","issue":"3","quality_controlled":"1","_id":"22168","external_id":{"arxiv":["2307.16611"]},"publisher":"Cambridge University Press","oa_version":"Preprint","month":"04"},{"date_created":"2026-06-29T10:53:47Z","year":"2023","citation":{"apa":"Conlon, D., Fox, J., &#38; Wigderson, Y. (2023). Off-diagonal book Ramsey numbers. <i>Combinatorics, Probability and Computing</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0963548322000360\">https://doi.org/10.1017/s0963548322000360</a>","ista":"Conlon D, Fox J, Wigderson Y. 2023. Off-diagonal book Ramsey numbers. Combinatorics, Probability and Computing. 32(3), 516–545.","ama":"Conlon D, Fox J, Wigderson Y. Off-diagonal book Ramsey numbers. <i>Combinatorics, Probability and Computing</i>. 2023;32(3):516-545. doi:<a href=\"https://doi.org/10.1017/s0963548322000360\">10.1017/s0963548322000360</a>","ieee":"D. Conlon, J. Fox, and Y. Wigderson, “Off-diagonal book Ramsey numbers,” <i>Combinatorics, Probability and Computing</i>, vol. 32, no. 3. Cambridge University Press, pp. 516–545, 2023.","short":"D. Conlon, J. Fox, Y. Wigderson, Combinatorics, Probability and Computing 32 (2023) 516–545.","mla":"Conlon, David, et al. “Off-Diagonal Book Ramsey Numbers.” <i>Combinatorics, Probability and Computing</i>, vol. 32, no. 3, Cambridge University Press, 2023, pp. 516–45, doi:<a href=\"https://doi.org/10.1017/s0963548322000360\">10.1017/s0963548322000360</a>.","chicago":"Conlon, David, Jacob Fox, and Yuval Wigderson. “Off-Diagonal Book Ramsey Numbers.” <i>Combinatorics, Probability and Computing</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/s0963548322000360\">https://doi.org/10.1017/s0963548322000360</a>."},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2110.14483","open_access":"1"}],"publication":"Combinatorics, Probability and Computing","author":[{"full_name":"Conlon, David","first_name":"David","last_name":"Conlon"},{"first_name":"Jacob","last_name":"Fox","full_name":"Fox, Jacob"},{"full_name":"Wigderson, Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","first_name":"Yuval","last_name":"Wigderson"}],"date_updated":"2026-07-14T08:27:40Z","abstract":[{"lang":"eng","text":"The book graph 𝐵(𝑘)\r\n𝑛 consists of 𝑛 copies of 𝐾𝑘+1 joined along a common 𝐾𝑘. In the prequel to this paper, we studied the diagonal Ramsey number 𝑟⁡(𝐵(𝑘)\r\n𝑛,𝐵(𝑘)\r\n𝑛). Here we consider the natural off-diagonal variant 𝑟⁡(𝐵(𝑘)\r\n𝑐⁢𝑛,𝐵(𝑘)\r\n𝑛) for fixed 𝑐 ∈(0,1]. In this more general setting, we show that an interesting dichotomy emerges: for very small 𝑐, a simple 𝑘-partite construction dictates the Ramsey function and all nearly-extremal colourings are close to being 𝑘-partite, while, for 𝑐 bounded away from 0, random colourings of an appropriate density are asymptotically optimal and all nearly-extremal colourings are quasirandom. Our investigations also open up a range of questions about what happens for intermediate values of 𝑐.\r\n\r\n"}],"scopus_import":"1","doi":"10.1017/s0963548322000360","date_published":"2023-05-01T00:00:00Z","day":"01","_id":"22165","month":"05","oa_version":"Preprint","publisher":"Cambridge University Press","external_id":{"arxiv":["2110.14483"]},"intvolume":"        32","volume":32,"publication_identifier":{"issn":["0963-5483"],"eissn":["1469-2163"]},"article_type":"original","quality_controlled":"1","issue":"3","extern":"1","OA_type":"green","type":"journal_article","status":"public","fulldoi":"https://doi.org/10.1017/s0963548322000360","arxiv":1,"title":"Off-diagonal book Ramsey numbers","publication_status":"published","page":"516-545","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"oa":1,"article_processing_charge":"No","mathsc":["05C55","05D10"],"OA_place":"repository","keyword":["Ramsey theory","book graphs","Ramsey goodness"]},{"volume":358,"publication_identifier":{"eissn":["1778-3569"],"issn":["1631-073X"]},"article_type":"original","intvolume":"       358","extern":"1","issue":"8","quality_controlled":"1","_id":"22182","external_id":{"arxiv":["2005.04135"]},"oa_version":"Preprint","month":"12","publisher":"Académie des Sciences","doi":"10.5802/crmath.101","date_published":"2020-12-03T00:00:00Z","day":"03","scopus_import":"1","abstract":[{"lang":"eng","text":"We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girão."}],"publication":"Comptes Rendus Mathématique","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2005.04135","open_access":"1"}],"year":"2020","date_created":"2026-06-29T11:00:09Z","citation":{"apa":"Fox, J., Wigderson, Y., &#38; Zhao, Y. (2020). A short proof of the canonical polynomial van der Waerden theorem. <i>Comptes Rendus Mathématique</i>. Académie des Sciences. <a href=\"https://doi.org/10.5802/crmath.101\">https://doi.org/10.5802/crmath.101</a>","ama":"Fox J, Wigderson Y, Zhao Y. A short proof of the canonical polynomial van der Waerden theorem. <i>Comptes Rendus Mathématique</i>. 2020;358(8):957-959. doi:<a href=\"https://doi.org/10.5802/crmath.101\">10.5802/crmath.101</a>","ista":"Fox J, Wigderson Y, Zhao Y. 2020. A short proof of the canonical polynomial van der Waerden theorem. Comptes Rendus Mathématique. 358(8), 957–959.","mla":"Fox, Jacob, et al. “A Short Proof of the Canonical Polynomial van Der Waerden Theorem.” <i>Comptes Rendus Mathématique</i>, vol. 358, no. 8, Académie des Sciences, 2020, pp. 957–59, doi:<a href=\"https://doi.org/10.5802/crmath.101\">10.5802/crmath.101</a>.","short":"J. Fox, Y. Wigderson, Y. Zhao, Comptes Rendus Mathématique 358 (2020) 957–959.","ieee":"J. Fox, Y. Wigderson, and Y. Zhao, “A short proof of the canonical polynomial van der Waerden theorem,” <i>Comptes Rendus Mathématique</i>, vol. 358, no. 8. Académie des Sciences, pp. 957–959, 2020.","chicago":"Fox, Jacob, Yuval Wigderson, and Yufei Zhao. “A Short Proof of the Canonical Polynomial van Der Waerden Theorem.” <i>Comptes Rendus Mathématique</i>. Académie des Sciences, 2020. <a href=\"https://doi.org/10.5802/crmath.101\">https://doi.org/10.5802/crmath.101</a>."},"date_updated":"2026-07-14T09:19:20Z","author":[{"first_name":"Jacob","last_name":"Fox","full_name":"Fox, Jacob"},{"full_name":"Wigderson, Yuval","last_name":"Wigderson","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5"},{"last_name":"Zhao","first_name":"Yufei","full_name":"Zhao, Yufei"}],"OA_place":"repository","page":"957-959","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"mathsc":["05D10","11B30"],"article_processing_charge":"No","oa":1,"fulldoi":"https://doi.org/10.5802/crmath.101","arxiv":1,"title":"A short proof of the canonical polynomial van der Waerden theorem","publication_status":"published","OA_type":"green","type":"journal_article","status":"public"},{"publication":"The Electronic Journal of Combinatorics","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1910.06287"}],"citation":{"ista":"He X, Wigderson Y. 2020. Multicolor Ramsey numbers via pseudorandom graphs. The Electronic Journal of Combinatorics. 27(1), P1.32.","ama":"He X, Wigderson Y. Multicolor Ramsey numbers via pseudorandom graphs. <i>The Electronic Journal of Combinatorics</i>. 2020;27(1). doi:<a href=\"https://doi.org/10.37236/9071\">10.37236/9071</a>","apa":"He, X., &#38; Wigderson, Y. (2020). Multicolor Ramsey numbers via pseudorandom graphs. <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/9071\">https://doi.org/10.37236/9071</a>","chicago":"He, Xiaoyu, and Yuval Wigderson. “Multicolor Ramsey Numbers via Pseudorandom Graphs.” <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics, 2020. <a href=\"https://doi.org/10.37236/9071\">https://doi.org/10.37236/9071</a>.","short":"X. He, Y. Wigderson, The Electronic Journal of Combinatorics 27 (2020).","ieee":"X. He and Y. Wigderson, “Multicolor Ramsey numbers via pseudorandom graphs,” <i>The Electronic Journal of Combinatorics</i>, vol. 27, no. 1. The Electronic Journal of Combinatorics, 2020.","mla":"He, Xiaoyu, and Yuval Wigderson. “Multicolor Ramsey Numbers via Pseudorandom Graphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 27, no. 1, P1.32, The Electronic Journal of Combinatorics, 2020, doi:<a href=\"https://doi.org/10.37236/9071\">10.37236/9071</a>."},"year":"2020","date_created":"2026-06-29T12:06:14Z","date_updated":"2026-07-14T09:42:53Z","author":[{"full_name":"He, Xiaoyu","first_name":"Xiaoyu","last_name":"He"},{"last_name":"Wigderson","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","first_name":"Yuval","full_name":"Wigderson, Yuval"}],"day":"01","date_published":"2020-02-01T00:00:00Z","doi":"10.37236/9071","abstract":[{"lang":"eng","text":"A weakly optimal Ks-free (n,d,λ)-graph is ad-regular Ks-free graph on n vertices with d= Θ(n1−α) and spectral expansion λ= Θ(n1−(s−1)α),  for some fixed α >0.  Such a graph is called optimal if additionally α=12s−3.  We prove that if s1,...,sk>3 are fixed positive integers and weakly optimal Ksi-free pseudorandom graphs exist for each 1<i<k, then the multicolor Ramsey numbers satisfy \r\n\r\nΩ(tS+1log2St)6r(s1,...,sk,t)6O(tS+1logSt),\r\nas t→∞, where S=∑ki=1(si−2). This generalizes previous results of Mubayi andVerstraete, who proved the case k= 1, and Alon and Rodl, who proved the cases1=···=sk= 3.  Both previous results used the existence of optimal rather than weakly optimal Ksi-free graphs"}],"scopus_import":"1","_id":"22185","external_id":{"arxiv":["1910.06287"]},"publisher":"The Electronic Journal of Combinatorics","oa_version":"Preprint","month":"02","article_type":"original","publication_identifier":{"eissn":["1077-8926"]},"volume":27,"intvolume":"        27","article_number":"P1.32","extern":"1","issue":"1","quality_controlled":"1","type":"journal_article","OA_type":"green","status":"public","arxiv":1,"fulldoi":"https://doi.org/10.37236/9071","publication_status":"published","title":"Multicolor Ramsey numbers via pseudorandom graphs","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","mathsc":["05C55","05D10"],"oa":1,"OA_place":"repository"}]