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On the chromaticity of certain subgraphs of a q-tree. (English) Zbl 0698.05029
It is known that the chromatic polynomial of triangulated graphs has only integral roots, but the converse doesn’t hold. The author gives here a new family of graphs for which the converse is also true. Namely, he proved that a graph G on $$n\geq q+1$$ vertices (q$$\geq 2)$$ has the chromatic polynomial $$P(G;\lambda)=\lambda (\lambda -1)...(\lambda -q+2)(\lambda - q+1)^ 2(\lambda -q)^{n-q-1}$$ if and only if G is obtained from a q- tree on n vertices by deleting an edge contained in exactly q-1 triangles; furthermore such a graph is triangulated.
Reviewer: C.Radu

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
chromatic polynomial; triangulated graphs; q-tree
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##### References:
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