2020/06/28 by Kostochka, Alexandr, Lavrov, Mikhail, Luo, Ruth +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2006.15730
A hypergraph \mathcal H is super-pancyclic if for each A ⊆ V(\mathcal H) with |A| ≥ 3, \mathcal H contains a Berge cycle with base vertex set A. We present two natural necessary conditions for a hypergraph to be super-pancyclic, and show that in several classes of hypergraphs these necessary conditions are also sufficient for this. In particular, they are sufficient for every hypergraph \mathcal H with δ(\mathcal H)≥ max\|V(\mathcal H)|, (|E(\mathcal H)|+10)/(4)\. We also consider super-cyclic bipartite graphs: those are (X,Y)-bigraphs G such that for each A ⊆ X with |A| ≥ 3, G has a cycle CA such that V(CA)∩ X=A. Such graphs are incidence graphs of super-pancyclic hypergraphs, and our proofs use the language of such graphs.