Upper Bound for the Coefficients of Chromatic polynomials

Simple item page
dc.creatorChang, Shu-Chiuan
dc.date2001-02-27
dc.date.accessioned2026-07-25T23:09:10Z
dc.descriptionThis paper describes an improvement in the upper bound for the magnitude of a coefficient of a term in the chromatic polynomial of a general graph. If $a_r$ is the coefficient of the $q^r$ term in the chromatic polynomial $P(G,q)$, where $q$ is the number of colors, then we find $a_r \le {e \choose v-r} - {e-g+2 \choose v-r-g+2} + {e-k_g-g+2 \choose v-r-g+2} - \sum _{n=1}^{k_g-\ell_g}\sum_{m=1}^{\ell_g-1} {e-g+1-n-m \choose v-r-g} - δ_{g,3}\sum_{n=1}^{k_g+\ell_{g+1}^*-\ell_g} {e-\ell_g-g+1-n \choose v-r-g}$, where $k_g$ is the number of circuits of length $g$ and $\ell_g$ and $\ell_{g+1}^*$ are certain numbers defined in the text.
dc.description9 pages, Latex
dc.identifierhttps://arxiv.org/abs/math/0102214
dc.identifierhttp://arxiv.org/abs/math/0102214
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/95866
dc.subjectCombinatorics
dc.subject05C15
dc.titleUpper Bound for the Coefficients of Chromatic polynomials
dc.typetext

Files

Collections

arXiv