New Results on Degree Sequences of Uniform Hypergraphs

A sequence of nonnegative integers is k-graphic if it is the degree sequence of a kuniform hypergraph. The only known characterization of k-graphic sequences is due to Dewdney in 1975. As this characterization does not yield an efficient algorithm, it is a fundamental open question to determine a more practical characterization. While several necessary conditions appear in the literature, there are few conditions that imply a sequence is k-graphic. In light of this, we present sharp sufficient conditions for k-graphicality based on a sequence’s length and degree sum. Kocay and Li gave a family of edge exchanges (an extension of 2-switches) that could be used to transform one realization of a 3-graphic sequence into any other realization. We extend their result to k-graphic sequences for all k > 3. Finally we give several applications of edge exchanges in hypergraphs, including generalizing a result of Busch et al. on packing graphic sequences.