@article{b83c36d023924d659e50757f27b74b56,
title = "Longest cycles in 3-connected hypergraphs and bipartite graphs",
abstract = "In the language of hypergraphs, our main result is a Dirac-type bound: We prove that every 3-connected hypergraph (Formula presented.) with (Formula presented.) has a hamiltonian Berge cycle. This is sharp and refines a conjecture by Jackson from 1981 (in the language of bipartite graphs). Our proofs are in the language of bipartite graphs, since the incidence graph of each hypergraph is bipartite.",
keywords = "degree conditions, longest cycles, pancyclic hypergraphs",
author = "Alexandr Kostochka and Mikhail Lavrov and Ruth Luo and Dara Zirlin",
note = "We thank the referees for their helpful comments. Alexandr Kostochka research was supported in part by NSF Grant DMS-1600592, NSF RTG Grant DMS-1937241, and Grants 18-01-00353A and 19-01-00682 of the Russian Foundation for Basic Research. Ruth Luo research was supported in part by NSF Grants DMS-1600592 and DMS-1902808. Dara Zirlin research was supported in part by Arnold O. Beckman Research Award (UIUC) RB20003 and by NSF RTG Grant DMS-1937241. We thank the referees for their helpful comments. Alexandr Kostochka research was supported in part by NSF Grant DMS\textbackslash{}u20101600592, NSF RTG Grant DMS\textbackslash{}u20101937241, and Grants 18\textbackslash{}u201001\textbackslash{}u201000353A and 19\textbackslash{}u201001\textbackslash{}u201000682 of the Russian Foundation for Basic Research. Ruth Luo research was supported in part by NSF Grants DMS\textbackslash{}u20101600592 and DMS\textbackslash{}u20101902808. Dara Zirlin research was supported in part by Arnold O. Beckman Research Award (UIUC) RB20003 and by NSF RTG Grant DMS\textbackslash{}u20101937241.",
year = "2022",
month = apr,
doi = "10.1002/jgt.22762",
language = "English (US)",
volume = "99",
pages = "758--782",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "Wiley-Liss Inc.",
number = "4",
}