有界度图上色多项式的无复零点区域
Regions without complex zeros for chromatic polynomials on graphs with bounded degree
摘要：
本文证明了最大度为$\D$的有限图$\mathbb{G}$的色多项式$P_\mathbb{G}(q)$对于具有$$ C^*(\D) = \min_{0<x<2^{1\over \D}-1} {(1+x)^{\D-1}\over x [2-(1+x)^\D]} $$的$\card q\ge C^*(\D)$是无零点的，改进了Sokal（2001）和Borgs（2005）的结果.此外，我们提出了一个加强这个条件的图没有三角形自由顶点。
英文摘要：
We 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
