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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
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