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All wheels with two missing consecutive spokes are chromatically unique. (English) Zbl 0957.05043

Summary: This paper shows that every wheel of order \(n\), \(n\geq 6\), with two missing consecutive spokes is chromatically unique.

MSC:

05C15 Coloring of graphs and hypergraphs
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References:

[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] Dirac, G. A., On rigid circuit graphs, Abh. Math. Sem. UNiv. Hamburgh, 25, 71-76 (1967) · Zbl 0098.14703
[4] Dong, F. M., On the chromatic uniqueness of generalized wheel graphs, J. Math. Res. Exposition, 10, 76-83 (1990), (in Chinese)
[5] Dong, F. M., On the chromatic uniqueness of two families of graphs, Acta Math. Sinica, 34, 242-251 (1991), (in Chinese) · Zbl 0753.05034
[6] F.M. Dong, Y.P. Liu and K.M. Koh, Almost all wheels with one missing spoke are chromatically unique, submitted.; F.M. Dong, Y.P. Liu and K.M. Koh, Almost all wheels with one missing spoke are chromatically unique, submitted.
[7] Farrell, E. J., On chromatic coefficients, Discrete Math., 29, 257-264 (1980) · Zbl 0443.05041
[8] Koh, K. M.; Teo, K. L., The search for chromatically unique graphs, Graphs Combin., 6, 259-285 (1990) · Zbl 0727.05023
[9] Read, R. C., An introduction to chromatic polynomials, J. Combin. Theory, 4, 52-71 (1968) · Zbl 0173.26203
[10] Tutte, W. T., (Graph Theory (1984), Addison-Wesley: Addison-Wesley Reading, MA) · Zbl 0554.05001
[11] Whitehead, E. G.; Zhao, L. C., Cutpoints and the chromatic polynomial, J. Graph Theory, 8, 371-377 (1984) · Zbl 0551.05041
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