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-connectedProof. Without loss of generality, let i = 1. We first show that x j

Pósa-Type Results for Berge Hypergraphs

“…For a hypergraph H consider the incidence bipartite graph G(A, B), where the vertices in A represent vertices of H and the vertices in B represent hyperedges of H. A vertex a ∈ A is adjacent with a vertex b ∈ B in G if and only if the vertex in H corresponding to a is contained in the hyperedge corresponding to b in H. There is a one-to-one correspondence between cycles in G and Berge cycles of H. The corresponding cycle in G of a Hamiltonian Berge cycle in H is a cycle containing all vertices of the set A. In [17,18,25,21,22] is related work on cycles covering color classes in bipartite graphs. In the coming subsections, we present the motivation for this work and introduce some necessary definitions and notions.…”