On a Generalization of Interval Edge Colorings of Graphs

Abstract

An interval edge (t; h) – coloring (h 2 Z+) of a graph G is a proper coloring α of edges of G with colors 1, 2..., t such that at least one edge of G is colored by i; i = 1, 2..., t and the colors of edges incident with each vertex v satisfy the condition dG(v) – 1≤ max S (v, α) – min S (v, α)≤dG (v) + h – 1, where dG(v) is the degree of a vertex v and S (v, α) is the set of colors of edges incident with v. In this paper we investigate some properties of interval edge (t; h) – colorings.