Please use this identifier to cite or link to this item: https://doi.org/10.1017/S0963548308009449
Title: Bounds for the real zeros of chromatic polynomials
Authors: Dong, F.M.
Koh, K.M. 
Issue Date: Nov-2008
Citation: Dong, F.M., Koh, K.M. (2008-11). Bounds for the real zeros of chromatic polynomials. Combinatorics Probability and Computing 17 (6) : 749-759. ScholarBank@NUS Repository. https://doi.org/10.1017/S0963548308009449
Abstract: Sokal in 2001 proved that the complex zeros of the chromatic polynomial PG(q) of any graph G lie in the disc |q| < 7.963907δ, where δ is the maximum degree of G. This result answered a question posed by Brenti, Royle and Wagner in 1994 and hence proved a conjecture proposed by Biggs, Damerell and Sands in 1972. Borgs gave a short proof of Sokal's result. Fernández and Procacci recently improved Sokal's result to |q| < 6.91δ. In this paper, we shall show that all real zeros of PG(q) are in the interval [0,5.664δ). For the special case that δ = 3, all real zeros of PG(q) are in the interval [0,4.765δ). © 2008 Cambridge University Press.
Source Title: Combinatorics Probability and Computing
URI: http://scholarbank.nus.edu.sg/handle/10635/102953
ISSN: 09635483
DOI: 10.1017/S0963548308009449
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