Paul Brooks

(VCU)

*Ryser's Conjecture and Special Cases*

(VCU)

**Abstract**. A matching of a graph *G* is a subset of edges such that no two edges share a vertex. A cover *C* is a set of vertices such that every edge has at least one vertex in* C. * König's theorem states that for bipartite graphs (graphs with no odd cycles) the size of a maximum matching is equal to the size of a minimum cover. Ryser's conjecture concerns an extension of the theorem to *r*-uniform *r*-partite hypergraphs. Matching and covering are presented from a mathematical programming point of view, Ryser's conjecture is presented, and special cases are discussed.