A note on chromatic roots of clique-theta graphs

Details A note on chromatic roots of clique-theta graphs A note on chromatic roots of clique-theta graphs

2011-08-13

arxiv.org/abs/1108.2808v1

Mathematics

Combinatorics

Scientific paper

We describe a family of graphs obtained by blowing up all but one of the
vertices of a generalised theta graph into cliques. We give a formula for the
chromatic polynomial of an arbitrary member of this family, and use this to
show that, if $\alpha$ is a chromatic root of a generalised theta graph, then
$p\alpha$ is a chromatic root for all natural numbers $p$.

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