Local edge coloring of graphs

Abstract

Let be a graph. A local edge coloring of G is a proper edge coloring such that for each subset S of E(G) with there exist edges such that where ns is the number of copies of P3 in the edge induced subgraph The maximum color assigned by a local edge coloring c to an edge of G is called the value of c and is denoted by The local edge chromatic number of G is where the minimum is taken over all local edge colorings c of G. In this article, we derive bounds and many results based on local edge coloring.

Keywords

• coloring
• edge coloring
• local coloring
• line graph