Defective colorings on k-uniform hypergraphs

Abstract

In this article, we introduce the concepts of proper coloring, defective coloring and defective coloring without monochromatic cycle on hypergraphs together with their chromatic numbers. Properties and relationship among these three types of coloring on hypergraphs are explored. Chromatic number of each type of coloring for several hypergraphs, espeacially, complete k-uniform hypergraph on n vertices and a complete r-partite k-uniform hypergraph are given. Lower bounds of the defective chromatic number of a hypergraph involving its clique number are provided.