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On planar and non-planar graphs having no chromatic zeros in the interval(1,2). (English) Zbl 1148.05025
A chromatic zero of a graph \(G\) is a zero of the chromatic polynomial of \(G\). A near-triangulation is a loopless connected plane graph having at most one non-triangular face. The authors describe a family of 2-connected graphs closed under certain operations and having no chromatic zeros in \((1,2)\). The family contains collections of graphs avoiding certain minors and also collections of plane graphs, including near-triangulation found by G. Birkhoff and D. G. Lewis [Trans. Am. Math. Soc. 60, 355–451 (1946; Zbl 0060.41601)].
05C10 Planar graphs; geometric and topological aspects of graph theory
05C15 Coloring of graphs and hypergraphs
Full Text: DOI
[1] Birkhoff, G.D.; Lewis, D.C., Chromatic polynomials, Trans. amer. math. soc., 60, 355-451, (1946) · Zbl 0060.41601
[2] R. Diestel, Graph Theory, second ed., Graduate Texts in Mathematics, vol. 173. Springer, New York, 2000.
[3] Dong, F.M.; Koh, K.M., On graphs having no chromatic zeros in the interval \((1, 2)\), SIAM J. discrete math., 20, 3, 799-810, (2006) · Zbl 1124.05032
[4] Dong, F.M.; Koh, K.M.; Teo, K.L., Chromatic polynomials and chromaticity of graphs, (2005), World Scientific Singapore · Zbl 1070.05038
[5] Jackson, B., A zero-free interval for chromatic polynomials of graphs, Combin. probab. comput., 2, 325-336, (1993) · Zbl 0794.05030
[6] Read, R.C.; Tutte, W.T., Chromatic polynomials, (), 15-42 · Zbl 0667.05022
[7] Royle, G., Private communication, (2007)
[8] Thomassen, C., The zero-free intervals for chromatic polynomials of graphs, Combin. probab. comput., 6, 4497-4506, (1997)
[9] Wakelin, C.D.; Woodall, D.R., Chromatic polynomials, polygon trees and outerplanar graphs, J. graphs theory, 16, 459-466, (1992) · Zbl 0778.05074
[10] Woodall, D.R., Zeros of chromatic polynomials, (), 199-223 · Zbl 0357.05044
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