Consider all the graphs with $n$ vertices and whose chromatic number is $k$, note that the graph does not have to be connected. What are the graphs with the maximal chromatic polynomial among those graphs? I think that the answer should be the graphs consisting of a $k$-clique plus $n-k$ isolated vertices, is it true? How to prove this?
2026-04-06 14:11:27.1775484687
Maximal chromatic polynomial of a graph with fixed chromatic number
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