论文标题
在串联平行图的色度零的位置
On the location of chromatic zeros of series-parallel graphs
论文作者
论文摘要
在本文中，我们考虑了串联平行图的色度多项式的零。补充Sokal的结果，显示磁盘$ | Q-1 | \ leq1 $之外的密度，我们在半平面$ \ re（q）> 3/2 $中显示了这些零的密度，我们在其中显示了一个含有间隔$（0,32/27）的开放式$ u $，因此$ \ u \ u \ u \ u \ u \ seTminus \ Z $ notem y ryos的notem y ryomes的notem串联平行图。 我们还通过证明每个足够大的整数$δ$都存在一个串联平行图来反驳Sokal的猜想，该图的所有顶点都具有该图，但最多都具有$δ$，并且其色度多项式的实际部分超过$δ$。
In this paper we consider the zeros of the chromatic polynomial of series-parallel graphs. Complementing a result of Sokal, showing density outside the disk $|q-1|\leq1$, we show density of these zeros in the half plane $\Re(q)>3/2$ and we show there exists an open region $U$ containing the interval $(0,32/27)$ such that $U\setminus\{1\}$ does not contain zeros of the chromatic polynomial of series-parallel graphs. We also disprove a conjecture of Sokal by showing that for each large enough integer $Δ$ there exists a series-parallel graph for which all vertices but one have degree at most $Δ$ and whose chromatic polynomial has a zero with real part exceeding $Δ$.
