Subdegrees and Chromatic Numbers of Hypergraphs

Abstract

The chromatic number χ(H) of a hypergraph H is studied in relation with the degrees of the vertices of H and of the section hypergraphs of H. The subdegree of a vertex xj of H is defined as the smallest integer k such that a sequential supression of the vertices of degree ⩽k suppresses xj. Bounds on the chromatic number χ(H) and on the independence number α(H) of H are obtained in terms of subdegrees. An algorithm for coloring H in χ(H) colors is proposed and computational experience is reported on.