Abstract:

We present various generalizations to hypergraphs of the celebrated Dirac theorem from 1952 guaranteeing a Hamilton cycle in every graph with minimum degree at least n/2.

A (tight) Hamilton cycle in a k-uniform hypergraph is a cyclic ordering of all vertices in which every k consecutive vertices form an edge of the hypergraph.

In particular, we present new results by Rodl, Rucinski, and Szemeredi on the relation between the minimum (k-1)-wise co-degree of a k-uniform hypergraph and the presence of a Hamilton cycle.