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The Zero-Free Intervals for Chromatic Polynomials of Graphs

Published online by Cambridge University Press:  01 December 1997

CARSTEN THOMASSEN
Affiliation:
Mathematical Institute, Technical University of Denmark, DK-2800 Lyngby, Denmark; (e-mail: C.Thomassen@mat.dtu.dk)

Abstract

The maximal zero-free intervals for chromatic polynomials of graphs are precisely (−∞, 0), (0, 1), (1, 32/27]. We also investigate the distribution of zeros of chromatic polynomials in various classes of graphs closed under minors. For example, the zeros of chromatic polynomials of graphs of tree-width at most k consist of 0, 1 and a dense subset of the interval (32/27, k].

Type
Research Article
Copyright
1997 Cambridge University Press

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