2019/05/09 by Kostochka, Alexandr, Luo, Ruth, Zirlin, Dara · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1905.03758
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 ⊆ V(\mathcal H) with |A| ≥ 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.