Conditions for a bigraph to be super-cyclic

Alexandr Kostochka, Mikhail Lavrov, Ruth Luo, Dara Zirlin

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Article numberP1.2
Pages (from-to)1-19
Number of pages19
JournalElectronic Journal of Combinatorics
Volume28
Issue number1
DOIs
StatePublished - 2021

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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