Algorithms for Finding Distance-Edge-Colorings of Graphs
Takehiro Ito, Akira Kato, Xiao Zhou, Takao Nishizeki · Medical Entomology and Zoology · 2005
For a bounded integer @?, we wish to color all edges of a graph G so that any two edges within distance @? have different colors. Such a coloring is called a distance-edge-coloring or an @?-edge-coloring of G. The distance-edge-coloring problem is to compute the minimum number of colors required for a distance-edge-coloring of a given graph G. A partial k-tree is a graph with tree-width bounded by a fixed constant k. We first present a polynomial-time exact algorithm to solve the problem for partial k-trees, and then give a polynomial-time 2-approximation algorithm for planar graphs.