Algorithms for finding distance-edge-colorings of graphs

Authors:
Takehiro Ito;Akira Kato;Xiao Zhou;Takao Nishizeki
Affiliations:
Graduate School of Information Sciences, Tohoku University, Aoba-yama 6-6-05, Sendai, 980-8579, Japan;Graduate School of Information Sciences, Tohoku University, Aoba-yama 6-6-05, Sendai, 980-8579, Japan;Graduate School of Information Sciences, Tohoku University, Aoba-yama 6-6-05, Sendai, 980-8579, Japan;Graduate School of Information Sciences, Tohoku University, Aoba-yama 6-6-05, Sendai, 980-8579, Japan
Venue:
Journal of Discrete Algorithms
Year:
2007

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Abstract

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.