A zero-free interval for chromatic polynomials
Discrete Mathematics - Special volume (part two) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs” (“The theory of regular graphs”)
The largest real zero of the chromatic polynomial
CPRT '94 Proceedings of the conference on Chromatic polynomials and related topics
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Journal of Combinatorial Theory Series B
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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].