A Linear Time Algorithm for Solving the Incidence Coloring Problem of Chordal Graphs

Abstract

An incidence of G consists of a vertex and one of its incident edge in G. The incidence coloring problem is a variation of vertex coloring problem. The problem is to find the minimum number (called incidence coloring number) of colors needed to dye every incidence of G so that the adjacent incidences do not dye the same color. A graph G is called a chordal (or triangulated) graph if and only if there is no induced cycle of length greater than 3 in G. In this paper, we propose a linear time algorithm for incidence-coloring a chordal graph. Further, we prove that the incidence coloring number of a chordal graph is Δ(G)+1, where Δ(G) is the maximum degree of G.