Chromatic Equivalence Classes of Some Families of Complete Tripartite Graphs
نویسندگان
چکیده
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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تاریخ انتشار 2013