Abstract: | We show that a graph G on n ? q + 1 vertices (where q ? 2) has the chromatic polynomial P(G;λ) = λ(λ ? 1) … (λ ? q + 2) (λ ? q + 1)2 (λ ? q)n?q?1 if and only if G can be obtained from a q-tree Ton n vertices by deleting an edge contained in exactly q ? 1 triangles of T. Furthermore, we prove that these graphs are triangulated. |