@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\u20101600592, NSF RTG Grant DMS\u20101937241, and Grants 18\u201001\u201000353A and 19\u201001\u201000682 of the Russian Foundation for Basic Research. Ruth Luo research was supported in part by NSF Grants DMS\u20101600592 and DMS\u20101902808. Dara Zirlin research was supported in part by Arnold O. Beckman Research Award (UIUC) RB20003 and by NSF RTG Grant DMS\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",
}