Chromatic polynomials of complementary (n,k)-clique pairs
Combinatorics
2011-06-08 v3
Abstract
We introduce a class of pairs of graphs consisting of two cliques joined by an arbitrary number of edges. The members of a pair have the property that the clique-bridging edge-set of one graph is the complement of that of the other. We prove a precise relation between the chromatic polynomials of the graphs in such a pair, showing that they have the same splitting field, and that the number of acyclic orientations of each graph is determined by the number of proper vertex-colourings of the other.
Cite
@article{arxiv.1012.3847,
title = {Chromatic polynomials of complementary (n,k)-clique pairs},
author = {Adam Bohn},
journal= {arXiv preprint arXiv:1012.3847},
year = {2011}
}
Comments
Replaced by a longer version, containing this note as a subsection