Abstract
AbstractLet be a simple graph with and be its chromatic polynomial. For an ordering of elements of , let be the number of integers , where , with either or . Let be the set of subsets of , where , which induces a subgraph of with as its only edge. We show that if and only if , where the sum runs over all orderings of . To prove this result, we establish an analogous result on order polynomials of posets and apply Stanley's work on the relation between chromatic polynomials and order polynomials.
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