Chromaticity of triangulated graphs
Paul Vaderlind · Journal of Graph Theory · 1988
Abstract It is shown here that a connected graph G without subgraphs isomorphic to K4 is triangulated if and only if its chromatic polynomial P(G,λ) equals λ(λ − 1)m(λ − 2)r for some integers m ≧ 1, r ≧ 0. This result generalizes the characterization of Two‐Trees given by E.G. Whitehead [“Chromaticity of Two‐Trees,” Journal of Graph Theory 9 (1985) 279–284].