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Rank and chromatic number of a graph

✍ Scribed by Kotlov, Andrei?

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 105 KB
Volume: 26
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199709)26:1<1::aid-jgt1>3.0.co;2-n

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✦ Synopsis

It was proved (A. Kotlov and L. Lovász, The rank and size of graphs, J. Graph Theory 23 (1996), 185-189) that the number of vertices in a twin-free graph is O(( √ 2) r ) where r is the rank of the adjacency matrix. This bound was shown to be tight. We show that the chromatic number of a graph is o(∆ r ) where ∆ = 4/3 < √ 2.

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