Chromatic equivalence classes of some families of complete tripartite graphs

Chia, G. L. and Ho, Chee-Kit * (2014) Chromatic equivalence classes of some families of complete tripartite graphs. Bulletin of the Malaysian Mathematical Sciences Society, 37 (3). pp. 641-646.

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Abstract

We obtain new necessary conditions on a graph which shares the same chromatic polynomial as that of the complete tripartite graph Km,n,r. Using these, we establish the chromatic equivalence classes for K1,n,n+1 (where n ≥ 2). This gives a partial solution to a question raised earlier by the authors. With the same technique, we further show that Kn−3,n,n+1 is chromatically unique if n ≥ 5. In the more general situation, we show that if 2 ≤ m ≤ n, then Km,n,n+1 is chromatically unique if n is sufficiently large.

Item Type: Article
Additional Information: First author is with the Institute of Mathematical Sciences, University of Malaya; second author is with the Dept. of Financial Mathematics and Statistics, Sunway University Business School
Uncontrolled Keywords: complete tripartite graph; chromatic polynomial; chromatic equivalence
Subjects: Q Science > QA Mathematics
Divisions: Sunway University > Sunway University Business School > Dept. Financial Mathematics & Statistics
Depositing User: Ms. Molly Chuah
Date Deposited: 02 Apr 2015 14:34
Last Modified: 02 Apr 2015 14:34
URI: http://eprints.sunway.edu.my/id/eprint/273

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