Document Type
Preprint
Publication Date
3-1-2021
Journal / Book Title
Combinatorics Probability and Computing
Abstract
In this note we study the emergence of Hamiltonian Berge cycles in random r-uniform hypergraphs. For we prove an optimal stopping time result that if edges are sequentially added to an initially empty r-graph, then as soon as the minimum degree is at least 2, the hypergraph with high probability has such a cycle. In particular, this determines the threshold probability for Berge Hamiltonicity of the ErdÅ s-Rényi random r-graph, and we also show that the 2-out random r-graph with high probability has such a cycle. We obtain similar results for weak Berge cycles as well, thus resolving a conjecture of Poole.
DOI
10.1017/S0963548320000437
MSU Digital Commons Citation
Bal, Deepak; Berkowitz, Ross; Devlin, Pat; and Schacht, Mathias, "Hamiltonian Berge cycles in random hypergraphs" (2021). Department of Mathematics Faculty Scholarship and Creative Works. 229.
https://digitalcommons.montclair.edu/mathsci-facpubs/229