Chromatic equivalence classes of some families of complete tripartite graphs

• Main Authors: Chia, G. L., Ho, Chee-Kit *
• Format: Article
• Language: English
• Published: Malaysian Mathematical Sciences Society 2014
• Subjects: QA Mathematics
• Online Access: http://eprints.sunway.edu.my/273/1/Chromatic%20equivalence_HoCK%20%282%29.pdf; http://eprints.sunway.edu.my/273/; http://www.emis.de/journals/BMMSS/pdf/v37n3/v37n3p3.pdf

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.