The edge cover chromatic index of complete tripartite graphs

Abstract

Let G(V, E) be a simple graph. For a k edge coloring C of G: E → {1,2,..., k}, let c _i(υ) denote the number of edges of G incident with vertex υ receiving color i. C is called an edge cover coloring, if for each vertex υ ∈ V, c _i(υ) ≥ 1 for i = 1,2,..., k. The maximum positive integer k such that G has a k edge cover coloring is called the edge cover chromatic index of G and is denoted by χ _c(G). The minimum degree of a graph G is denoted by δ. A graph G is said to be of class CI if χ _c(G) = δ and otherwise of class CII. We show a characterization of class CI complete tripartite graph that allows for an efficient determination of its edge cover chromatic index.