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February 2008 Complementary Graphs and the Chromatic Number
Colin L. Starr, Galen E. Turner III
Missouri J. Math. Sci. 20(1): 19-26 (February 2008). DOI: 10.35834/mjms/1316032831

Abstract

Zykov proved that if $G$ and $\overline G$ are complementary graphs having chromatic numbers $\chi$ and $\overline \chi$, respectively then $\chi \cdot {\overline \chi}$ is at least the number of vertices of $G$. Nordhaus and Gaddum gave an upper bound for $\chi \cdot {\overline \chi}$ and gave both upper and lower bounds for the analogue $\chi + {\overline \chi}$. In this paper we characterize those graphs for which $\chi \cdot {\overline \chi}$ and $\chi+\overline{\chi}$ reach the bounds of Nordhaus and Gaddum.

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Colin L. Starr. Galen E. Turner III. "Complementary Graphs and the Chromatic Number." Missouri J. Math. Sci. 20 (1) 19 - 26, February 2008. https://doi.org/10.35834/mjms/1316032831

Information

Published: February 2008
First available in Project Euclid: 14 September 2011

zbMATH: 1145.05309
Digital Object Identifier: 10.35834/mjms/1316032831

Subjects:
Primary: 05C15

Rights: Copyright © 2008 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.20 • No. 1 • February 2008
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