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Chromatic uniqueness of the complements of certain forests. (English) Zbl 0878.05031
A $$T$$-shape tree is a tree with the degree sequence $$\{ 1,1,1,2,2,\dots, 2,3\}$$. By studying adjoint polynomials, the authors obtained the following result. There is a family $$\mathcal H$$ of $$T$$-shape trees such that for each $$H \in {\mathcal H}$$, if the complement of a graph $$G$$ is a disjoint union of any number of copies of $$H$$, then $$G$$ is chromatically unique.
##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C05 Trees
##### Keywords:
chromatic unique; adjoint polynomial; chromatic polynomial; tree
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##### References:
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