Conditions for a bigraph to be super-cyclic (Q2223452)

Summary: A hypergraph \(\mathcal H\) is super-pancyclic if for each \(A \subseteq V(\mathcal{H})\) with \(|A| \geqslant 3, \mathcal{H}\) 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. In particular, they are sufficient for every hypergraph \(\mathcal{H}\) with \(\delta(\mathcal{H})\geqslant \max\{|V(\mathcal{H})|, \frac{|E(\mathcal H)|+10}{4}\} \). We also consider super-cyclic bipartite graphs: \((X,Y)\)-bigraphs \(G\) such that for each \(A \subseteq X\) with \(|A| \geqslant 3, G\) has a cycle \(C_A\) such that \(V(C_A)\cap X=A\). Such graphs are incidence graphs of super-pancyclic hypergraphs, and our proofs use the language of such graphs.