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Proof of a Chromatic Polynomial Conjecture

✍ Scribed by F.M. Dong

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 138 KB
Volume: 78
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1999.1925

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✦ Synopsis

Let P(G, *) denote the chromatic polynomial of a graph G. It is proved in this paper that for every connected graph G of order n and real number * n, (*&2) n&1 P(G, *)&*(*&1) n&2 P(G, *&1) 0. By this result, the following conjecture proposed by Bartels and Welsh is proved: P(G, n)(P(G, n&1)) &1 >e for every graph G of order n.

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