Abstract
Many combinatorial problems can be efficiently solved for partial k-trees. The edge-coloring problem is one of a few combinatorial problems for which no linear-time algorithm has been obtained for partial k-trees. The best known algorithm solves the problem for partial k-trees G in time \(O\left( {n\Delta ^{2^{2\left( {k + 1} \right)} } } \right)\) where n is the number of vertices and Δ is the maximum degree of G. This paper gives a linear algorithm which optimally edge-colors a given partial k-tree for fixed k.
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Zhou, X., Nakano, Si., Nishizeki, T. (1993). A linear algorithm for edge-coloring partial k-trees. In: Lengauer, T. (eds) Algorithms—ESA '93. ESA 1993. Lecture Notes in Computer Science, vol 726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57273-2_76
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DOI: https://doi.org/10.1007/3-540-57273-2_76
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