zbMATH — the first resource for mathematics

The chromaticity of certain graphs with five triangles. (English) Zbl 0787.05040
Summary: Let \(W(n,k)\) denote the graph of order \(n\) obtained from the wheel \(W_ n\) by deleting all but \(k\) consecutive spokes. We study the chromaticity of graphs which share certain properties of \(W(n,6)\) which can be obtained from the coefficients of the chromatic polynomial of \(W(n,6)\). In particular, we prove that \(W(n,6)\) is chromatically unique for all integers \(n\geq 8\). We also obtain two additional families of chromatically unique graphs.

05C15 Coloring of graphs and hypergraphs
Full Text: DOI
[1] Chao, C.Y.; Whitehead, E.G., Chromatically unique graphs, Discrete math., 27, 171-177, (1979) · Zbl 0411.05035
[2] Chia, G.L., The chromaticity of wheels with a missing spoke, Discrete math., 82, 209-212, (1990) · Zbl 0712.05025
[3] Farrell, E.J., On chromatic coefficients, Discrete math., 29, 257-264, (1980) · Zbl 0443.05041
[4] K.M. Koh and C.P. Teo, The chromaticity of graphs related to broken wheels, to appear. · Zbl 0752.05029
[5] Read, R.C., An introduction to chromatic polynomials, J. combin. theory, 4, 52-71, (1968) · Zbl 0173.26203
[6] Read, R.C., A note on the chromatic uniqueness of W10, Discrete math., 69, 317, (1988) · Zbl 0639.05019
[7] Whitehead, E.G.; Zhao, L.C., Cutpoints and the chromatic polynomial, J. graph theory, 8, 371-377, (1984) · Zbl 0551.05041
[8] Whitney, H., The coloring of graphs, Ann. math., 33, 688-718, (1932) · JFM 58.0606.01
[9] Woodall, D.R., Zeros of chromatic polynomials, (), 199-223 · Zbl 0357.05044
[10] Xu, S.J.; Li, N.Z., The chromaticity of wheels, Discrete math., 51, 207-212, (1984) · Zbl 0547.05032
[11] Zykov, A.A., On some properties of linear complexes, Amer. math. soc. transl. no. 79, Math. sb., 24, 66, 163-188, (1949)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.