2001/02/27 by Shu-Chiuan Chang, Chang, Shu-Chiuan
Mathematics · #05C15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #math.CO #msc:05C15
paper · pdf · doi:10.48550/arxiv.math/0102214
9 pages, Latex
arxiv created 2001/02/27 · openalex publication_date 2001/02/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This 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 ar is the coefficient of the qr term in the chromatic polynomial P(G,q), where q is the number of colors, then we find ar ≤ e \choose v-r - e-g+2 \choose v-r-g+2 + e-kg-g+2 \choose v-r-g+2 - ∑ n=1kg-ℓg∑m=1ℓg-1 e-g+1-n-m \choose v-r-g - δg,3∑n=1^kg+ℓg+1^*-ℓg e-ℓg-g+1-n \choose v-r-g, where kg is the number of circuits of length g and ℓg and ℓg+1^* are certain numbers defined in the text.