Conditions for a bigraph to be super-cyclic

Alexandr Kostochka, University of Illinois Urbana-Champaign
Mikhail Lavrov, Kennesaw State University
Ruth Luo, University of California, San Diego
Dara Zirlin, University of Illinois Urbana-Champaign


A hypergraph H is super-pancyclic if for each A ⊆ V (H) with |A| ≽ 3, 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 H with δ(H) ≽ max{|V (H)|,|E(H)|+10 4 }. We also consider super-cyclic bipartite graphs: (X, Y )-bigraphs G such that for each A ⊆ X with |A| ≽ 3, G has a cycle CA such that V (CA) ∩ X = A. Super-cyclic graphs are incidence graphs of super-pancyclic hypergraphs, and our proofs use the language of such graphs.