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Pairs of Chromatically Equivalent Graphs

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Abstract

Two graphs are said to be chromatically equivalent if they have the same chromatic polynomial. In this paper we give the means to construct infinitely many pairs of chromatically equivalent graphs where one graph in the pair is clique-separable, that is, can be obtained by identifying an r-clique in some graph H 1 with an r-clique in some graph H 2, and the other graph is non-clique-separable. There are known methods for finding pairs of chromatically equivalent graphs where both graphs are clique-separable or both graphs are non-clique-separable. Although examples of pairs of chromatically equivalent graphs where only one of the graphs is clique-separable are known, a method for the construction of infinitely many such pairs was not known. Our method constructs such pairs of graphs with odd order n ≥ 9.

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  1. Kerri Morgan

    Present address: Department of Computer Science and Software Engineering, The University of Melbourne, Melbourne, VIC, 3010, Australia

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  1. Clayton School of Information Technology, Monash University, Melbourne, VIC, 3800, Australia

    Kerri Morgan

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  1. Kerri Morgan
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Correspondence to Kerri Morgan.

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Morgan, K. Pairs of Chromatically Equivalent Graphs. Graphs and Combinatorics 27, 547–556 (2011). https://doi.org/10.1007/s00373-010-0984-z

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  • DOI: https://doi.org/10.1007/s00373-010-0984-z

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