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A note on chromatic uniqueness of graphs. (English) Zbl 0616.05035
There is shown that if simple graph G is chromatically unique, then G has at most two blocks. Furthermore, in the case that G has two blocks, they are both vertex transitive and chromatically unique. Let G be a graph consisting of two blocks H and \(K_ 2\). Then G is chromatically unique iff H is chromatically unique and vertex transitive. This answers of Whitehead and Zhao’s conjecture in the affirmative.
Reviewer: J.Fiamčík

MSC:
05C15 Coloring of graphs and hypergraphs
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References:
[1] Graph Theory, Addison-Wesley, Reading MA (1969).
[2] Read, J. Combinatorial Theory 4 pp 52– (1968) · Zbl 0165.32802
[3] Whitehead, J. Graph Theory 8 pp 371– (1984)
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