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

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 assigned to every incidence of G so that the adjacent incidences are not assigned the same color. In this paper, we propose a linear time algorithm for incidence-coloring a strongly chordal graph when a strong elimination ordering is given. Further, we prove that the incidence coloring number of a strongly chordal graph is ∆(G) + 1, where ∆(G) is the maximum degree of G.