Chromatic equivalence classes of some families of complete tripartite graphs
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....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Malaysian Mathematical Sciences Society
2014
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| Online Access: | http://eprints.sunway.edu.my/273/ http://eprints.sunway.edu.my/273/1/Chromatic%20equivalence_HoCK%20%282%29.pdf |
| Summary: | 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.
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