hypergraph

A generalization of Vizing's Theorem? ★★

Author(s): Rosenfeld

Conjecture   Let be a simple -uniform hypergraph, and assume that every set of points is contained in at most edges. Then there exists an -edge-coloring so that any two edges which share vertices have distinct colors.

Keywords: edge-coloring; hypergraph; Vizing

Ryser's conjecture ★★★

Author(s): Ryser

Conjecture   Let be an -uniform -partite hypergraph. If is the maximum number of pairwise disjoint edges in , and is the size of the smallest set of vertices which meets every edge, then .

Keywords: hypergraph; matching; packing