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Hybrid evolutionary algorithm for the b-chromatic number

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Abstract

The b-chromatic number of a graph \(G\) is a maximum integer \(\varphi (G)\) for which there exists a proper \(\varphi (G)\)-coloring with the additional property that each color class contains a vertex that is adjacent to one of the vertices within each color class. In contrast to many theoretical results discovered over the last decade and a half there are no computer running experiments on \(\varphi (G)\) in the literature. This work presents a hybrid evolutionary algorithm for graph b-coloring. Its performance has been tested on some instances of regular graphs where their b-chromatic number is theoretically known in advance, as well as by comparing with a brute force algorithm solving the regular graphs up to 12 vertices. In addition, the algorithm has been tested on some larger graphs taken from a DIMACS challenge benchmark that also proved to be challenging for the algorithms searching for the classical chromatic number \(\chi (G)\).

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova ulica 17, 2000, Maribor, Slovenia

    Iztok Fister, Iztok Peterin, Marjan Mernik & Matej Črepinšek

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  1. Iztok Fister
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  2. Iztok Peterin
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  3. Marjan Mernik
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  4. Matej Črepinšek
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Correspondence to Iztok Fister.

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Fister, I., Peterin, I., Mernik, M. et al. Hybrid evolutionary algorithm for the b-chromatic number. J Heuristics 21, 501–521 (2015). https://doi.org/10.1007/s10732-015-9288-z

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