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arXiv · 1905.03758

Super-pancyclic hypergraphs and bipartite graphs

Alexandr Kostochka·Ruth Luo·Dara Zirlin
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Abstract

We find Dirac-type sufficient conditions for a hypergraph $\mathcal H$ with few edges to be hamiltonian. We also show that these conditions provide that $\mathcal H$ is {\em super-pancyclic}, i.e., for each $A \subseteq V(\mathcal H)$ with $|A| \geq 3$, $\mathcal H$ contains a Berge cycle with vertex set $A$. We mostly use the language of bipartite graphs, because every bipartite graph is the incidence graph of a multihypergraph. In particular, we extend some results of Jackson on the existence of long cycles in bipartite graphs where the vertices in one part have high minimum degree. Furthermore, we prove a conjecture of Jackson from 1981 on long cycles in 2-connected bipartite graphs.

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Alexandr Kostochka, Ruth Luo, Dara Zirlin. 2019-05-09. Super-pancyclic hypergraphs and bipartite graphs. https://arxiv.org/abs/1905.03758

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