[{"has_accepted_license":"1","ddc":["500"],"doi":"10.1002/rsa.70095","arxiv":1,"department":[{"_id":"MaKw"},{"_id":"GradSch"}],"article_number":"e70095","publication_identifier":{"eissn":["1098-2418"],"issn":["1042-9832"]},"publication":"Random Structures and Algorithms","external_id":{"arxiv":["2506.23970"]},"title":"Approximate Itai–Zehavi conjecture for random graphs","license":"https://creativecommons.org/licenses/by/4.0/","das_tickbox":"0","publication_status":"published","publisher":"Wiley","year":"2026","OA_place":"publisher","citation":{"apa":"Hollom, L., Lichev, L., Mond, A., Portier, J., &#38; Wang, Y. (2026). Approximate Itai–Zehavi conjecture for random graphs. <i>Random Structures and Algorithms</i>. Wiley. <a href=\"https://doi.org/10.1002/rsa.70095\">https://doi.org/10.1002/rsa.70095</a>","mla":"Hollom, Lawrence, et al. “Approximate Itai–Zehavi Conjecture for Random Graphs.” <i>Random Structures and Algorithms</i>, vol. 69, no. 2, e70095, Wiley, 2026, doi:<a href=\"https://doi.org/10.1002/rsa.70095\">10.1002/rsa.70095</a>.","short":"L. Hollom, L. Lichev, A. Mond, J. Portier, Y. Wang, Random Structures and Algorithms 69 (2026).","ista":"Hollom L, Lichev L, Mond A, Portier J, Wang Y. 2026. Approximate Itai–Zehavi conjecture for random graphs. Random Structures and Algorithms. 69(2), e70095.","ieee":"L. Hollom, L. Lichev, A. Mond, J. Portier, and Y. Wang, “Approximate Itai–Zehavi conjecture for random graphs,” <i>Random Structures and Algorithms</i>, vol. 69, no. 2. Wiley, 2026.","chicago":"Hollom, Lawrence, Lyuben Lichev, Adva Mond, Julien Portier, and Yiting Wang. “Approximate Itai–Zehavi Conjecture for Random Graphs.” <i>Random Structures and Algorithms</i>. Wiley, 2026. <a href=\"https://doi.org/10.1002/rsa.70095\">https://doi.org/10.1002/rsa.70095</a>.","ama":"Hollom L, Lichev L, Mond A, Portier J, Wang Y. Approximate Itai–Zehavi conjecture for random graphs. <i>Random Structures and Algorithms</i>. 2026;69(2). doi:<a href=\"https://doi.org/10.1002/rsa.70095\">10.1002/rsa.70095</a>"},"oa_version":"Published Version","scopus_import":"1","file":[{"file_name":"2026_RandomStructAlgorithms_Hollom.pdf","date_updated":"2026-10-07T07:10:43Z","file_size":457581,"checksum":"9a786460a47542f24576e947987e558a","file_id":"23068","content_type":"application/pdf","relation":"main_file","creator":"dernst","access_level":"open_access","success":1,"date_created":"2026-10-07T07:10:43Z"}],"project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","grant_number":"101076777","name":"Randomness and structure in combinatorics"}],"fulldoi":"https://doi.org/10.1002/rsa.70095","volume":69,"language":[{"iso":"eng"}],"date_updated":"2026-10-07T07:13:30Z","month":"09","PlanS_conform":"1","oa":1,"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","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","day":"01","date_published":"2026-09-01T00:00:00Z","abstract":[{"text":"A famous conjecture by Itai and Zehavi states that, for every 𝑑\r\n-vertex-connected graph 𝐺\r\n and every vertex 𝑟\r\n in 𝐺\r\n, there are 𝑑\r\n spanning trees of 𝐺\r\n such that, for every vertex 𝑣\r\n in 𝐺 ∖{𝑟}\r\n, the paths between 𝑟\r\n and 𝑣\r\n in different trees are internally vertex-disjoint. We show that with high probability the Itai–Zehavi conjecture holds asymptotically for the Erdős–Rényi random graph 𝐺⁡(𝑛,𝑝)\r\n when 𝑛⁢𝑝 =𝜔⁡(log⁡𝑛)\r\n and for random regular graphs 𝐺⁡(𝑛,𝑑)\r\n when 𝑑 =𝜔⁡(log⁡𝑛)\r\n. Moreover, we essentially confirm the conjecture up to a constant factor for sparser random regular graphs. This answers a question of Draganić and Krivelevich positively. Our proof makes use of recent developments on sprinkling techniques in random regular graphs.","lang":"eng"}],"file_date_updated":"2026-10-07T07:10:43Z","acknowledgement":"Hollom was supported by the Internal Graduate Studentship of Trinity College, Cambridge. Mond was supported by UK Research and Innovation grant MR/W007320/2. Wang was supported by the ERC Starting Grant “RANDSTRUCT” No. 101076777. Lichev was supported by the Austrian Science Fund (FWF) [10.55776/ESP624]. For open access purposes, the authors have applied a CC BY public copyright license to any author-accepted manuscript version arising from this submission. Open Access funding provided by Technische Universitat Wien.\r\n\r\nPart of this research was done during a visit of the fourth author to IST Austria. We thank IST Austria for its hospitality. We also thank the anonymous referees for their comments and suggestions. Open Access funding provided by Technische Universitat Wien. This work was supported by the European Research Council, UK Research and Innovation, the Austrian Science Fund, and Trinity College.","intvolume":"        69","OA_type":"hybrid","researchdata_availability":"no","author":[{"last_name":"Hollom","full_name":"Hollom, Lawrence","first_name":"Lawrence"},{"full_name":"Lichev, Lyuben","last_name":"Lichev","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","first_name":"Lyuben"},{"last_name":"Mond","full_name":"Mond, Adva","first_name":"Adva"},{"first_name":"Julien","full_name":"Portier, Julien","last_name":"Portier"},{"first_name":"Yiting","id":"1917d194-076e-11ed-97cd-837255f88785","last_name":"Wang","full_name":"Wang, Yiting"}],"article_type":"original","issue":"2","type":"journal_article","supplementarymaterial":"yes","article_processing_charge":"Yes (via OA deal)","status":"public","_id":"23001","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2026-09-27T22:01:52Z"},{"date_published":"2025-01-06T00:00:00Z","oa":1,"quality_controlled":"1","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","short":"CC BY (4.0)","image":"/images/cc_by.png"},"day":"06","month":"01","date_updated":"2025-09-30T10:28:07Z","OA_type":"hybrid","abstract":[{"text":"Let f(r)(n;s,k) denote the maximum number of edges in an n-vertex r-uniform hypergraph containing no subgraph with k edges and at most s vertices. Brown, Erdős and Sós [New directions in the theory of graphs (Proc. Third Ann Arbor Conf., Univ. Michigan 1971), pp. 53--63, Academic Press 1973] conjectured that the limit limn→∞n−2f(3)(n;k+2,k) exists for all k. The value of the limit was previously determined for k=2 in the original paper of Brown, Erdős and Sós, for k=3 by Glock [Bull. Lond. Math. Soc. 51 (2019) 230--236] and for k=4 by Glock, Joos, Kim, Kühn, Lichev and Pikhurko [arXiv:2209.14177, accepted by Proc. Amer. Math. Soc.] while Delcourt and Postle [arXiv:2210.01105, accepted by Proc. Amer. Math. Soc.] proved the conjecture (without determining the limiting value).\r\nIn this paper, we determine the value of the limit in the Brown-Erdős-Sós Problem for k∈{5,6,7}. More generally, we obtain the value of limn→∞n−2f(r)(n;rk−2k+2,k) for all r≥3 and k∈{5,6,7}. In addition, by combining these new values with recent results of Bennett, Cushman and Dudek [arXiv:2309.00182] we obtain new asymptotic values for several generalised Ramsey numbers.","lang":"eng"}],"type":"journal_article","isi":1,"page":"1-43","article_type":"original","author":[{"first_name":"Stefan","last_name":"Glock","full_name":"Glock, Stefan"},{"first_name":"Jaehoon","last_name":"Kim","full_name":"Kim, Jaehoon"},{"id":"9aa8388e-d003-11ee-8458-c4c1d7447977","first_name":"Lyuben","last_name":"Lichev","full_name":"Lichev, Lyuben"},{"first_name":"Oleg","full_name":"Pikhurko, Oleg","last_name":"Pikhurko"},{"last_name":"Sun","full_name":"Sun, Shumin","first_name":"Shumin"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2025-02-10T08:39:46Z","_id":"19017","status":"public","article_processing_charge":"No","department":[{"_id":"MaKw"}],"arxiv":1,"ddc":["500"],"doi":"10.4153/s0008414x25000021","has_accepted_license":"1","title":"On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7","publication_status":"epub_ahead","external_id":{"isi":["001416788600001"],"arxiv":["2403.04474"]},"publication_identifier":{"eissn":["1496-4279"],"issn":["0008-414X"]},"publication":"Canadian Journal of Mathematics","OA_place":"publisher","publisher":"Cambridge University Press","year":"2025","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.4153/s0008414x25000021"}],"fulldoi":"https://doi.org/10.4153/s0008414x25000021","oa_version":"Published Version","scopus_import":"1","citation":{"ama":"Glock S, Kim J, Lichev L, Pikhurko O, Sun S. On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7. <i>Canadian Journal of Mathematics</i>. 2025:1-43. doi:<a href=\"https://doi.org/10.4153/s0008414x25000021\">10.4153/s0008414x25000021</a>","chicago":"Glock, Stefan, Jaehoon Kim, Lyuben Lichev, Oleg Pikhurko, and Shumin Sun. “On the (k + 2, k)-Problem of Brown, Erdős, and Sós for k = 5,6,7.” <i>Canadian Journal of Mathematics</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.4153/s0008414x25000021\">https://doi.org/10.4153/s0008414x25000021</a>.","ieee":"S. Glock, J. Kim, L. Lichev, O. Pikhurko, and S. Sun, “On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7,” <i>Canadian Journal of Mathematics</i>. Cambridge University Press, pp. 1–43, 2025.","ista":"Glock S, Kim J, Lichev L, Pikhurko O, Sun S. 2025. On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7. Canadian Journal of Mathematics., 1–43.","short":"S. Glock, J. Kim, L. Lichev, O. Pikhurko, S. Sun, Canadian Journal of Mathematics (2025) 1–43.","mla":"Glock, Stefan, et al. “On the (k + 2, k)-Problem of Brown, Erdős, and Sós for k = 5,6,7.” <i>Canadian Journal of Mathematics</i>, Cambridge University Press, 2025, pp. 1–43, doi:<a href=\"https://doi.org/10.4153/s0008414x25000021\">10.4153/s0008414x25000021</a>.","apa":"Glock, S., Kim, J., Lichev, L., Pikhurko, O., &#38; Sun, S. (2025). On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7. <i>Canadian Journal of Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.4153/s0008414x25000021\">https://doi.org/10.4153/s0008414x25000021</a>"}},{"external_id":{"arxiv":["2204.07376 "],"isi":["001420659400001"]},"title":"The semi-random tree process","publication_status":"published","article_number":"104120","publication":"European Journal of Combinatorics","publication_identifier":{"issn":["0195-6698"]},"arxiv":1,"department":[{"_id":"MaKw"}],"doi":"10.1016/j.ejc.2025.104120","volume":126,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2204.07376"}],"language":[{"iso":"eng"}],"citation":{"mla":"Burova, Sofiya, and Lyuben Lichev. “The Semi-Random Tree Process.” <i>European Journal of Combinatorics</i>, vol. 126, 104120, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">10.1016/j.ejc.2025.104120</a>.","apa":"Burova, S., &#38; Lichev, L. (2025). The semi-random tree process. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">https://doi.org/10.1016/j.ejc.2025.104120</a>","short":"S. Burova, L. Lichev, European Journal of Combinatorics 126 (2025).","ama":"Burova S, Lichev L. The semi-random tree process. <i>European Journal of Combinatorics</i>. 2025;126. doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">10.1016/j.ejc.2025.104120</a>","chicago":"Burova, Sofiya, and Lyuben Lichev. “The Semi-Random Tree Process.” <i>European Journal of Combinatorics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">https://doi.org/10.1016/j.ejc.2025.104120</a>.","ista":"Burova S, Lichev L. 2025. The semi-random tree process. European Journal of Combinatorics. 126, 104120.","ieee":"S. Burova and L. Lichev, “The semi-random tree process,” <i>European Journal of Combinatorics</i>, vol. 126. Elsevier, 2025."},"oa_version":"Preprint","scopus_import":"1","fulldoi":"https://doi.org/10.1016/j.ejc.2025.104120","OA_place":"repository","publisher":"Elsevier","year":"2025","OA_type":"green","abstract":[{"text":"The online semi-random graph process is a one-player game which starts with the empty graph on n vertices. At every round, a player (called Builder) is presented with a vertex v chosen uniformly at random and independently from previous rounds, and constructs an edge of their choice that is incident to v. Inspired by recent advances on the semi-random graph process, we define a family of generalized online semi-random models.\r\nWe analyse a particular instance that shares similar features with the original semi-random graph process and determine the hitting times of the classical graph properties minimum degree k,k-connectivity, containment of a perfect matching, a Hamiltonian cycle and an \r\nH-factor for a fixed graph H possessing an additional tree-like property. Along the way, we derive a few consequences of the famous Aldous-Broder algorithm that may be of independent interest.","lang":"eng"}],"acknowledgement":"We are grateful to Dieter Mitsche for related discussions and to several anonymous referees for multiple useful comments.","intvolume":"       126","oa":1,"quality_controlled":"1","day":"01","date_published":"2025-05-01T00:00:00Z","date_updated":"2025-09-30T10:28:42Z","month":"05","_id":"19018","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2025-02-10T09:00:53Z","article_processing_charge":"No","status":"public","isi":1,"type":"journal_article","author":[{"first_name":"Sofiya","full_name":"Burova, Sofiya","last_name":"Burova"},{"last_name":"Lichev","full_name":"Lichev, Lyuben","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","first_name":"Lyuben"}],"article_type":"original"},{"volume":8,"language":[{"iso":"eng"}],"scopus_import":"1","oa_version":"Published Version","citation":{"short":"L. Lichev, B. Schapira, Annales Henri Lebesgue 8 (2025) 35–65.","apa":"Lichev, L., &#38; Schapira, B. (2025). Color-avoiding percolation on the Erdős–Rényi random graph. <i>Annales Henri Lebesgue</i>. École normale supérieure de Rennes. <a href=\"https://doi.org/10.5802/ahl.228\">https://doi.org/10.5802/ahl.228</a>","mla":"Lichev, Lyuben, and Bruno Schapira. “Color-Avoiding Percolation on the Erdős–Rényi Random Graph.” <i>Annales Henri Lebesgue</i>, vol. 8, École normale supérieure de Rennes, 2025, pp. 35–65, doi:<a href=\"https://doi.org/10.5802/ahl.228\">10.5802/ahl.228</a>.","ieee":"L. Lichev and B. Schapira, “Color-avoiding percolation on the Erdős–Rényi random graph,” <i>Annales Henri Lebesgue</i>, vol. 8. École normale supérieure de Rennes, pp. 35–65, 2025.","ista":"Lichev L, Schapira B. 2025. Color-avoiding percolation on the Erdős–Rényi random graph. Annales Henri Lebesgue. 8, 35–65.","ama":"Lichev L, Schapira B. Color-avoiding percolation on the Erdős–Rényi random graph. <i>Annales Henri Lebesgue</i>. 2025;8:35-65. doi:<a href=\"https://doi.org/10.5802/ahl.228\">10.5802/ahl.228</a>","chicago":"Lichev, Lyuben, and Bruno Schapira. “Color-Avoiding Percolation on the Erdős–Rényi Random Graph.” <i>Annales Henri Lebesgue</i>. École normale supérieure de Rennes, 2025. <a href=\"https://doi.org/10.5802/ahl.228\">https://doi.org/10.5802/ahl.228</a>."},"fulldoi":"https://doi.org/10.5802/ahl.228","file":[{"access_level":"open_access","success":1,"date_created":"2025-06-23T11:59:22Z","date_updated":"2025-06-23T11:59:22Z","file_name":"2025_AnnalesHenriLebesgue_Lichev.pdf","checksum":"cca22d171b7affa010d17f5e793b0045","file_size":746588,"file_id":"19875","content_type":"application/pdf","relation":"main_file","creator":"dernst"}],"DOAJ_listed":"1","OA_place":"publisher","year":"2025","publisher":"École normale supérieure de Rennes","external_id":{"arxiv":["2211.16086 "]},"publication_status":"published","title":"Color-avoiding percolation on the Erdős–Rényi random graph","publication_identifier":{"eissn":["2644-9463"]},"publication":"Annales Henri Lebesgue","arxiv":1,"department":[{"_id":"MaKw"}],"has_accepted_license":"1","doi":"10.5802/ahl.228","ddc":["510"],"_id":"19859","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2025-06-22T22:02:07Z","article_processing_charge":"Yes","status":"public","type":"journal_article","author":[{"id":"9aa8388e-d003-11ee-8458-c4c1d7447977","first_name":"Lyuben","full_name":"Lichev, Lyuben","last_name":"Lichev"},{"full_name":"Schapira, Bruno","last_name":"Schapira","first_name":"Bruno"}],"corr_author":"1","page":"35-65","article_type":"original","OA_type":"gold","acknowledgement":"We thank Dieter Mitsche for enlightening discussions, Balázs Ráth for a number of comments\r\nand corrections on a first version of this paper, and an anonymous referee for several useful remarks.","intvolume":"         8","abstract":[{"lang":"eng","text":"We consider a recently introduced model of color-avoiding percolation (abbreviated CA-percolation) defined as follows. Every edge in a graph G is colored in some of k>=2 colors. Two vertices u and v in G are said to be CA-connected if u and v may be connected using any subset of k-1 colors. CA-connectivity defines an equivalence relation on the vertex set of G whose classes are called CA-components.\r\nWe study the component structure of a randomly colored Erdős–Rényi random graph of constant average degree. We distinguish three regimes for the size of the largest component: a supercritical regime, a so-called intermediate regime, and a subcritical regime, in which the largest CA-component has respectively linear, logarithmic, and bounded size. Interestingly, in the subcritical regime, the bound is deterministic and given by the number of colors."}],"file_date_updated":"2025-06-23T11:59:22Z","day":"01","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","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","oa":1,"date_published":"2025-06-01T00:00:00Z","date_updated":"2025-06-23T12:01:36Z","month":"06"},{"month":"11","PlanS_conform":"1","date_updated":"2026-09-16T07:00:33Z","date_published":"2025-11-01T00:00:00Z","oa":1,"day":"01","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","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","abstract":[{"lang":"eng","text":"We consider random two-player zero-sum dynamic games with perfect information on a class of infinite directed graphs. Starting from a fixed vertex, the players take turns to move a token along the edges of the graph. Every vertex is assigned a payoff known in advance by both players. Every time the token visits a vertex, Player 2 pays Player 1 the corresponding payoff. We consider a distribution over such games by assigning i.i.d. payoffs to the vertices. On the one hand, for acyclic directed graphs of bounded degree and sub-exponential expansion, we show that, when the duration of the game tends to infinity, the value converges almost surely to a constant at an exponential rate dominated in terms of the expansion. On the other hand, for the infinite d-ary tree (that does not fall into the previous class of graphs), we show convergence at a double-exponential rate."}],"file_date_updated":"2025-12-30T08:13:04Z","intvolume":"        15","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). This work was supported by the French Agence Nationale de la Recherche (ANR) under references ANR-21-CE40-0020 (CONVERGENCE project) and ANR-20-CE40-0002 (GrHyDy), by Fondecyt grant 1220174, by ANID Chile grant ACT210005, and by the ERC CoG 863818 (ForM-SMArt) grant. This collaboration was mainly conducted during a 1-year visit of Bruno Ziliotto to the Center for Mathematical Modeling (CMM) at University of Chile in 2023, under the IRL program of CNRS. This work was supported by Fondation CFM pour la Recherche. This paper has also been funded by the Agence Nationale de la Recherche under grant ANR-17-EURE-0010 (Investissements d’Avenir program).","OA_type":"hybrid","corr_author":"1","article_type":"original","page":"1517-1535","author":[{"first_name":"Luc","full_name":"Attia, Luc","last_name":"Attia"},{"last_name":"Lichev","full_name":"Lichev, Lyuben","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","first_name":"Lyuben"},{"first_name":"Dieter","full_name":"Mitsche, Dieter","last_name":"Mitsche"},{"id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","first_name":"Raimundo J","last_name":"Saona Urmeneta","full_name":"Saona Urmeneta, Raimundo J","orcid":"0000-0001-5103-038X"},{"last_name":"Ziliotto","full_name":"Ziliotto, Bruno","first_name":"Bruno"}],"isi":1,"type":"journal_article","status":"public","article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2025-04-06T22:01:32Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"20234"}]},"_id":"19508","ddc":["000"],"doi":"10.1007/s13235-025-00636-4","has_accepted_license":"1","department":[{"_id":"MaKw"},{"_id":"KrCh"}],"ec_funded":1,"publication":"Dynamic Games and Applications","publication_identifier":{"issn":["2153-0785"],"eissn":["2153-0793"]},"title":"Random zero-sum dynamic games on infinite directed graphs","publication_status":"published","external_id":{"isi":["001449708900001"]},"publisher":"Springer Nature","year":"2025","OA_place":"publisher","file":[{"access_level":"open_access","success":1,"date_created":"2025-12-30T08:13:04Z","file_name":"2025_DynGamesAppl_Attia.pdf","date_updated":"2025-12-30T08:13:04Z","file_size":570994,"checksum":"b3a1b7eef40c9ac2acf3fef563081694","file_id":"20891","content_type":"application/pdf","creator":"dernst","relation":"main_file"}],"project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}],"fulldoi":"https://doi.org/10.1007/s13235-025-00636-4","citation":{"ieee":"L. Attia, L. Lichev, D. Mitsche, R. J. Saona Urmeneta, and B. Ziliotto, “Random zero-sum dynamic games on infinite directed graphs,” <i>Dynamic Games and Applications</i>, vol. 15. Springer Nature, pp. 1517–1535, 2025.","ista":"Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. 2025. Random zero-sum dynamic games on infinite directed graphs. Dynamic Games and Applications. 15, 1517–1535.","chicago":"Attia, Luc, Lyuben Lichev, Dieter Mitsche, Raimundo J Saona Urmeneta, and Bruno Ziliotto. “Random Zero-Sum Dynamic Games on Infinite Directed Graphs.” <i>Dynamic Games and Applications</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s13235-025-00636-4\">https://doi.org/10.1007/s13235-025-00636-4</a>.","ama":"Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. Random zero-sum dynamic games on infinite directed graphs. <i>Dynamic Games and Applications</i>. 2025;15:1517-1535. doi:<a href=\"https://doi.org/10.1007/s13235-025-00636-4\">10.1007/s13235-025-00636-4</a>","apa":"Attia, L., Lichev, L., Mitsche, D., Saona Urmeneta, R. J., &#38; Ziliotto, B. (2025). Random zero-sum dynamic games on infinite directed graphs. <i>Dynamic Games and Applications</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s13235-025-00636-4\">https://doi.org/10.1007/s13235-025-00636-4</a>","mla":"Attia, Luc, et al. “Random Zero-Sum Dynamic Games on Infinite Directed Graphs.” <i>Dynamic Games and Applications</i>, vol. 15, Springer Nature, 2025, pp. 1517–35, doi:<a href=\"https://doi.org/10.1007/s13235-025-00636-4\">10.1007/s13235-025-00636-4</a>.","short":"L. Attia, L. Lichev, D. Mitsche, R.J. Saona Urmeneta, B. Ziliotto, Dynamic Games and Applications 15 (2025) 1517–1535."},"scopus_import":"1","oa_version":"Published Version","language":[{"iso":"eng"}],"volume":15},{"OA_place":"repository","DOAJ_listed":"1","year":"2024","publisher":"EMS Press","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2304.10930","open_access":"1"}],"fulldoi":"https://doi.org/10.4171/aihpd/200","citation":{"ieee":"I. Hartarsky, L. Lichev, and F. L. Toninelli, “Local dimer dynamics in higher dimensions,” <i>Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions</i>. EMS Press, 2024.","ista":"Hartarsky I, Lichev L, Toninelli FL. 2024. Local dimer dynamics in higher dimensions. Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions.","ama":"Hartarsky I, Lichev L, Toninelli FL. Local dimer dynamics in higher dimensions. <i>Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions</i>. 2024. doi:<a href=\"https://doi.org/10.4171/aihpd/200\">10.4171/aihpd/200</a>","chicago":"Hartarsky, Ivailo, Lyuben Lichev, and Fabio Lucio Toninelli. “Local Dimer Dynamics in Higher Dimensions.” <i>Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and Their Interactions</i>. EMS Press, 2024. <a href=\"https://doi.org/10.4171/aihpd/200\">https://doi.org/10.4171/aihpd/200</a>.","apa":"Hartarsky, I., Lichev, L., &#38; Toninelli, F. L. (2024). Local dimer dynamics in higher dimensions. <i>Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and Their Interactions</i>. EMS Press. <a href=\"https://doi.org/10.4171/aihpd/200\">https://doi.org/10.4171/aihpd/200</a>","mla":"Hartarsky, Ivailo, et al. “Local Dimer Dynamics in Higher Dimensions.” <i>Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and Their Interactions</i>, EMS Press, 2024, doi:<a href=\"https://doi.org/10.4171/aihpd/200\">10.4171/aihpd/200</a>.","short":"I. Hartarsky, L. Lichev, F.L. Toninelli, Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and Their Interactions (2024)."},"scopus_import":"1","oa_version":"Preprint","department":[{"_id":"MaKw"}],"arxiv":1,"doi":"10.4171/aihpd/200","publication_status":"epub_ahead","das_tickbox":"1","title":"Local dimer dynamics in higher dimensions","external_id":{"arxiv":["2304.10930"]},"publication":"Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions","publication_identifier":{"eissn":["2308-5835"],"issn":["2308-5827"]},"type":"journal_article","article_type":"original","author":[{"full_name":"Hartarsky, Ivailo","last_name":"Hartarsky","first_name":"Ivailo"},{"last_name":"Lichev","full_name":"Lichev, Lyuben","first_name":"Lyuben","id":"9aa8388e-d003-11ee-8458-c4c1d7447977"},{"first_name":"Fabio Lucio","last_name":"Toninelli","full_name":"Toninelli, Fabio Lucio"}],"date_created":"2025-01-29T10:57:09Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"18951","status":"public","article_processing_charge":"Yes","supplementarymaterial":"unclear","mathsc":["05B50","05C70","82C20"],"date_published":"2024-08-26T00:00:00Z","day":"26","quality_controlled":"1","oa":1,"month":"08","date_updated":"2026-10-16T10:14:21Z","researchdata_availability":"unclear","OA_type":"gold","abstract":[{"text":"We consider local dynamics of the dimer model (perfect matchings) on hypercubic boxes [n] \r\nd . These consist of successively switching the dimers along alternating cycles of prescribed (small) lengths. We study the connectivity properties of the dimer configuration space equipped with these transitions. Answering a question of Freire, Klivans, Milet, and Saldanha, we show that in three dimensions any configuration admits an alternating cycle of length at most 6. We further establish that any configuration on [n] d  features order n d−2  alternating cycles of length at most 4d−2. We also prove that the dynamics of dimer configurations on the unit hypercube of dimension d is ergodic when switching alternating cycles of length at most 4d−4. Finally, in the planar but non-bipartite case, we show that parallelogram-shaped boxes in the triangular lattice are ergodic for switching alternating cycles of lengths 4 and 6 only, thus improving a result of Kenyon and Rémila, which also uses 8-cycles. None of our proofs make reference to height functions.","lang":"eng"}]}]