Regions without complex zeros for chromatic polynomials on graphs with bounded degree

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dc.creatorFernandez, Roberto
dc.creatorProcacci, Aldo
dc.date2007-04-19
dc.date.accessioned2026-07-07T07:57:33Z
dc.date.available2026-07-07T07:57:33Z
dc.descriptionWe prove that the chromatic polynomial $P_\mathbb{G}(q)$ of a finite graph $\mathbb{G}$ of maximal degree $\D$ is free of zeros for $\card q\ge C^*(\D)$ with $$ C^*(\D) = \min_{0<x<2^{1\over \D}-1} {(1+x)^{\D-1}\over x [2-(1+x)^\D]} $$ This improves results by Sokal (2001) and Borgs (2005). Furthermore, we present a strengthening of this condition for graphs with no triangle-free vertices.
dc.description14 pages, to appear in Combinatorics, Probability and Computing
dc.identifierhttps://arxiv.org/abs/0704.2617
dc.identifierhttp://arxiv.org/abs/0704.2617
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127683
dc.subjectMathematical Physics
dc.subjectCombinatorics
dc.subject82B20; 05C15
dc.titleRegions without complex zeros for chromatic polynomials on graphs with bounded degree
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