Longest cycles in 3-connected hypergraphs and bipartite graphs

2020/04/17 by Kostochka, Alexandr, Lavrov, Mikhail, Luo, Ruth +1 · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.08291

Abstract

In the language of hypergraphs, our main result is a Dirac-type bound: we prove that every 3-connected hypergraph H with δ(H)≥ max\|V(H)|, (|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.

Cited by

• The Connected Bipartite Turán Problem for Long Cycles and Paths
• Berge k-Factors of Regular Hypergraphs

Related

• Super-pancyclic hypergraphs and bipartite graphs
• Dirac's Theorem for hamiltonian Berge cycles in uniform hypergraphs
• A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs
• Pósa-type results for Berge-hypergraphs
• A dirac-type theorem for berge cycles in random hypergraphs