Algorithms for finding distance-edge-colorings of graphs |
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Authors: | Takehiro Ito Akira Kato Xiao Zhou Takao Nishizeki |
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Institution: | aGraduate School of Information Sciences, Tohoku University, Aoba-yama 6-6-05, Sendai, 980-8579, Japan |
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Abstract: | For a bounded integer ℓ, we wish to color all edges of a graph G so that any two edges within distance ℓ have different colors. Such a coloring is called a distance-edge-coloring or an ℓ-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. |
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Keywords: | Algorithm Approximation algorithm Distance-edge-coloring Partial k-trees Planar graphs |
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