Chromatic Polynomials and the Symmetric Group
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.
KeywordsDirected Graph Symmetric Group Combinatorial Interpretation Chromatic Polynomial Cover Polynomial
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