华侨大学学报（自然科学版）2026，Vol.47Issue(3)：373-378,6.DOI:10.11830/ISSN.1000-5013.202508025
图的1-非正常着色多项式
On 1-Improper Chromatic Polynomial of Graph
摘要
Abstract
Firstly,a recursive formula for P1(G,x)is established by using the chromatic polynomials of the edge-contraction graphs of G,by which the explicit expressions of the 1-improper chromatic polynomial for complete graphs,cycles and trees are given.Secondly,the inclusion-exclusion formula of Pd(G,x)is given.Finally,Whitney's broken cycle theorem is generalized to P1(G,x),by which the first four coefficients of P1(G,x)are thereby determined.The result shows that the coefficients of the 1-improper chromatic polynom-i al are neither alternative in sign nor unimodal in general.关键词
色多项式/非正常着色多项式/对消结构/容斥原理Key words
chromatic polynomial/improper chromatic polynomial/cancellation structure/inclusion-exclusion principle分类
数理科学引用本文复制引用
赵佳丽,钱建国..图的1-非正常着色多项式[J].华侨大学学报（自然科学版）,2026,47(3):373-378,6.基金项目
国家自然科学基金资助项目(12361070) （12361070）
青海民族大学研究生创新项目(07M2024009) （07M2024009）
