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On q-trees. (English) Zbl 0591.05021
A q-tree is defined inductively as a complete graph \(K_ q\) on q vertices or as the graph G’ obtained from a q-tree G by adding a new vertex that is adjacent to all the vertices in some \(K_ q\) of G. The authors show that the chromatic polynomial \(P(G,\lambda)\) of a q-tree with n vertices \((n\geq q)\) is \(P(G,\lambda)=\lambda (\lambda - 1)...(\lambda -q+1)(\lambda -q)^{n-q}.\)
Reviewer: A.Tucker

MSC:
05C05 Trees
05C15 Coloring of graphs and hypergraphs
05C35 Extremal problems in graph theory
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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] Stirling numbers and coloring of q-trees, Prace Nauk. Inst. Mat. Politechn. Wroclaw, Ser. Stud. i Materi√Ĺ 13, Grafy, hipergrafy, system blokow (1977), pp. 63–67.
[4] Whitehead, J. Graph Theory 9 pp 279– (1985)
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