[{"volume":13,"scopus_import":"1","doi":"10.1017/fms.2024.68","citation":{"ama":"Gishboliner L, Shapira A, Wigderson Y. An efficient asymmetric removal lemma and its limitations. <i>Forum of Mathematics, Sigma</i>. 2025;13. doi:<a href=\"https://doi.org/10.1017/fms.2024.68\">10.1017/fms.2024.68</a>","apa":"Gishboliner, L., Shapira, A., &#38; Wigderson, Y. (2025). An efficient asymmetric removal lemma and its limitations. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2024.68\">https://doi.org/10.1017/fms.2024.68</a>","ista":"Gishboliner L, Shapira A, Wigderson Y. 2025. An efficient asymmetric removal lemma and its limitations. Forum of Mathematics, Sigma. 13, e38.","mla":"Gishboliner, Lior, et al. “An Efficient Asymmetric Removal Lemma and Its Limitations.” <i>Forum of Mathematics, Sigma</i>, vol. 13, e38, Cambridge University Press, 2025, doi:<a href=\"https://doi.org/10.1017/fms.2024.68\">10.1017/fms.2024.68</a>.","ieee":"L. Gishboliner, A. Shapira, and Y. Wigderson, “An efficient asymmetric removal lemma and its limitations,” <i>Forum of Mathematics, Sigma</i>, vol. 13. Cambridge University Press, 2025.","short":"L. Gishboliner, A. Shapira, Y. Wigderson, Forum of Mathematics, Sigma 13 (2025).","chicago":"Gishboliner, Lior, Asaf Shapira, and Yuval Wigderson. “An Efficient Asymmetric Removal Lemma and Its Limitations.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/fms.2024.68\">https://doi.org/10.1017/fms.2024.68</a>."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2301.07693"}],"quality_controlled":"1","oa_version":"Preprint","extern":"1","_id":"22158","arxiv":1,"article_type":"original","publication_identifier":{"issn":["2050-5094"]},"day":"10","external_id":{"arxiv":["2301.07693"]},"OA_place":"repository","author":[{"full_name":"Gishboliner, Lior","last_name":"Gishboliner","first_name":"Lior"},{"full_name":"Shapira, Asaf","first_name":"Asaf","last_name":"Shapira"},{"last_name":"Wigderson","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","full_name":"Wigderson, Yuval"}],"date_updated":"2026-07-08T10:31:22Z","title":"An efficient asymmetric removal lemma and its limitations","publisher":"Cambridge University Press","abstract":[{"text":"The triangle removal states that if G contains  edge-disjoint triangles, then G contains  triangles. Unfortunately, there are no sensible bounds on the order of growth of , and at any rate, it is known that  is not polynomial in . Csaba recently obtained an asymmetric variant of the triangle removal, stating that if G contains  edge-disjoint triangles, then G contains  copies of . To this end, he devised a new variant of Szemerédi’s regularity lemma. We obtain the following results:\r\n\r\n• We first give a regularity-free proof of Csaba’s theorem, which improves the number of copies of  to the optimal number .\r\n\r\n• We say that H is -abundant if every graph containing  edge-disjoint triangles has  copies of H. It is easy to see that a -abundant graph must be triangle-free and tripartite. Given our first result, it is natural to ask if all triangle-free tripartite graphs are -abundant. Our second result is that assuming a well-known conjecture of Ruzsa in additive number theory, the answer to this question is negative.\r\n\r\nOur proofs use a mix of combinatorial, number-theoretic, probabilistic and Ramsey-type arguments.","lang":"eng"}],"date_created":"2026-06-29T10:51:07Z","intvolume":"        13","language":[{"iso":"eng"}],"OA_type":"green","status":"public","month":"02","publication":"Forum of Mathematics, Sigma","mathsc":["05C35","11B75"],"oa":1,"type":"journal_article","year":"2025","article_processing_charge":"No","publication_status":"published","date_published":"2025-02-10T00:00:00Z","article_number":"e38","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"article_processing_charge":"No","year":"2021","publication_status":"published","date_published":"2021-01-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"1-15","oa":1,"type":"journal_article","issue":"1","month":"01","publication":"Journal of Combinatorics","status":"public","mathsc":["05C35","05C55"],"publisher":"International Press of Boston","date_created":"2026-06-29T10:52:13Z","abstract":[{"text":"Recently, Souza introduced blowup Ramsey numbers as a gener-\r\nalization of bipartite Ramsey numbers. For graphs G and H, say\r\nG r\r\n−→ H if every r-edge-coloring of G contains a monochromatic\r\ncopy of H. Let H[t] denote the t-blowup of H. Then the blowup\r\nRamsey number of G, H, r, and t is defined as the minimum n\r\nsuch that G[n] r\r\n−→ H[t]. Souza proved upper and lower bounds on\r\nn that are exponential in t, and conjectured that the exponential\r\nconstant does not depend on G. We prove that the dependence on\r\nG in the exponential constant is indeed unnecessary, but conjecture\r\nthat some dependence on G is unavoidable.\r\nAn important step in both Souza’s proof and ours is a theorem of\r\nNikiforov, which says that if a graph contains a constant fraction\r\nof the possible copies of H, then it contains a blowup of H of\r\nlogarithmic size. We also provide a new proof of this theorem with\r\na better quantitative dependence.","lang":"eng"}],"intvolume":"        12","language":[{"iso":"eng"}],"OA_type":"green","author":[{"last_name":"Fox","first_name":"Jacob","full_name":"Fox, Jacob"},{"last_name":"Luo","first_name":"Sammy","full_name":"Luo, Sammy"},{"full_name":"Wigderson, Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","last_name":"Wigderson","first_name":"Yuval"}],"date_updated":"2026-07-08T10:41:31Z","title":"Extremal and Ramsey results on graph blowups","arxiv":1,"publication_identifier":{"eissn":["2150-959X"],"issn":["2156-3527"]},"article_type":"original","day":"01","external_id":{"arxiv":["1912.08328"]},"OA_place":"repository","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.08328","open_access":"1"}],"quality_controlled":"1","oa_version":"Preprint","_id":"22161","extern":"1","volume":12,"scopus_import":"1","citation":{"ieee":"J. Fox, S. Luo, and Y. Wigderson, “Extremal and Ramsey results on graph blowups,” <i>Journal of Combinatorics</i>, vol. 12, no. 1. International Press of Boston, pp. 1–15, 2021.","mla":"Fox, Jacob, et al. “Extremal and Ramsey Results on Graph Blowups.” <i>Journal of Combinatorics</i>, vol. 12, no. 1, International Press of Boston, 2021, pp. 1–15, doi:<a href=\"https://doi.org/10.4310/joc.2021.v12.n1.a1\">10.4310/joc.2021.v12.n1.a1</a>.","ama":"Fox J, Luo S, Wigderson Y. Extremal and Ramsey results on graph blowups. <i>Journal of Combinatorics</i>. 2021;12(1):1-15. doi:<a href=\"https://doi.org/10.4310/joc.2021.v12.n1.a1\">10.4310/joc.2021.v12.n1.a1</a>","apa":"Fox, J., Luo, S., &#38; Wigderson, Y. (2021). Extremal and Ramsey results on graph blowups. <i>Journal of Combinatorics</i>. International Press of Boston. <a href=\"https://doi.org/10.4310/joc.2021.v12.n1.a1\">https://doi.org/10.4310/joc.2021.v12.n1.a1</a>","ista":"Fox J, Luo S, Wigderson Y. 2021. Extremal and Ramsey results on graph blowups. Journal of Combinatorics. 12(1), 1–15.","chicago":"Fox, Jacob, Sammy Luo, and Yuval Wigderson. “Extremal and Ramsey Results on Graph Blowups.” <i>Journal of Combinatorics</i>. International Press of Boston, 2021. <a href=\"https://doi.org/10.4310/joc.2021.v12.n1.a1\">https://doi.org/10.4310/joc.2021.v12.n1.a1</a>.","short":"J. Fox, S. Luo, Y. Wigderson, Journal of Combinatorics 12 (2021) 1–15."},"doi":"10.4310/joc.2021.v12.n1.a1"}]