Abstract
In this paper, we present a new algorithm for computing the chromatic polynomial of a general graph G. Our method is based on the addition of edges and contraction of non-edges of G, the base case of the recursion being chordal graphs. The set of edges to be considered is taken from a triangulation of G. To achieve our goal, we use the properties of triangulations and clique-trees with respect to the previous operations, and guide our algorithm to efficiently divide the original problem.
Furthermore, we give some lower bounds of the general complexity of our method, and provide experimental results for several families of graphs.
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Berthomé, P., Lebresne, S., Nguyễn, K. (2005). Computation of Chromatic Polynomials Using Triangulations and Clique Trees. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_32
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DOI: https://doi.org/10.1007/11604686_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31000-6
Online ISBN: 978-3-540-31468-4
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