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# Cutpoints and the chromatic polynomial

@article{Whitehead1984CutpointsAT, title={Cutpoints and the chromatic polynomial}, author={Earl Glen Whitehead and Lian-Chang Zhao}, journal={Journal of Graph Theory}, year={1984}, volume={8}, pages={371-377} }

- Published 1984 in Journal of Graph Theory
DOI:10.1002/jgt.3190080305

We prove that the multiplicity of the root 1 in the chromatic polynomial of a simple graph G is equal to the number of nontrivial blocks in G. In particular, a connected simple graph G has a cutpoint if and only if its chromatic polynomial is divisible by (A 1)'. We apply this theorem to obtain some chromatic equivalence and uniqueness results.