Longest cycles in 3-connected hypergraphs and bipartite graphs

Alexandr Kostochka; Dara Zirlin; Mikhail Lavrov; Ruth Luo

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Longest cycles in 3-connected hypergraphs and bipartite graphs

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arxiv 2004.08291 v1 pith:H33PPWP7 submitted 2020-04-17 math.CO

Longest cycles in 3-connected hypergraphs and bipartite graphs

Alexandr Kostochka , Mikhail Lavrov , Ruth Luo , Dara Zirlin This is my paper

classification math.CO

keywords bipartitegraphslanguageconnectedhypergraphhypergraphsbergebound

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In the language of hypergraphs, our main result is a Dirac-type bound: we prove that every $3$-connected hypergraph $H$ with $ \delta(H)\geq \max\{|V(H)|, \frac{|E(H)|+10}{4}\}$ 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.

Longest cycles in 3-connected hypergraphs and bipartite graphs

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