Combinatorics Seminar

A tight Hamilton cycle in a k-uniform hypergraph is a cyclic ordering of the vertices such that every k consecutive vertices form an edge. We solve the following problem (for large n): what is the minimum m such that if G is a k-uniform hypergraph on n vertices whose every k-1 vertices are in at least m edges (i.e., G has minimum codegree at least m), then G has a tight Hamilton cycle? We show that this minimum m is (n-k+2)/2, confirming a conjecture of Katona and Kierstead from 1999.

Joint work with Richard Lang, Arjun Ranganathan, and Nicolás Sanhueza-Matamala.