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Chromatic Polynomials and the Symmetric Group

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Abstract.

In this paper we give first a new combinatorial interpretation of the coefficients of chromatic polynomials of graphs in terms of subsets of permutations. Motivated by this new interpretation, we introduce next a combinatorially defined polynomial associated to a directed graph, and prove that it is related to chromatic polynomials. These polynomials are a specialization of cover polynomials of digraphs.

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Authors and Affiliations

  1. Indian Institute of Science, Mathematics Department, Bangalore, 560012, India

    Philippe Pitteloud

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  1. Philippe Pitteloud
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Correspondence to Philippe Pitteloud.

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I am grateful to the Swiss National Science Foundation for its partial financial support

Final version received: June 25, 2003

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Pitteloud, P. Chromatic Polynomials and the Symmetric Group. Graphs and Combinatorics 20, 131–144 (2004). https://doi.org/10.1007/s00373-003-0544-x

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  • DOI: https://doi.org/10.1007/s00373-003-0544-x

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