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The chromaticity of wheels with a missing spoke. II. (English) Zbl 0838.05052
Summary: In the previous paper [ibid. 82, No. 2, 209-212 (1990; Zbl 0712.05025)], it was shown that the graph \(U_{n+ 1}\) obtained from the wheel \(W_{n+ 1}\) by deleting a spoke is uniquely determined by its chromatic polynomial if \(n\geq 3\) is odd. In this paper, we show that the result is also true for even \(n\geq 4\) except when \(n= 6\) in which case, the graph \(W\) given in the paper is the only graph having the same chromatic polynomial as that of \(U_7\). The relevant tool is the notion of nearly uniquely colorable graph.

05C15 Coloring of graphs and hypergraphs
Full Text: DOI
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