• DOI:10.37236/9683
• Corpus ID: 220250386

Conditions for a Bigraph to be Super-Cyclic

@article{Kostochka2021ConditionsFA,
  title={Conditions for a Bigraph to be Super-Cyclic},
  author={Alexandr V. Kostochka and Mikhail Lavrov and Ruth Luo and Dara Zirlin},
  journal={Electron. J. Comb.},
  year={2021},
  volume={28},
  pages={1}
}

• A. Kostochka, Mikhail Lavrov, +1 author Dara Zirlin
• Published 28 June 2020
• Mathematics
• Electron. J. Comb.

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: those are $(X,Y)$-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.