论文标题
增强了erdős-lovásztihany的猜想
Enhancing the Erdős-Lovász Tihany Conjecture for line graphs of multigraphs
论文作者
论文摘要
在本文中，我们证明了Erdős-LovászTihany猜想的增强版本，用于多编码的线图。也就是说，对于每个图形$ g $，其色数$χ（g）$都比其集团数字$ω（g）$和非负整数$ \ ell $，任何两个整数$ s，t \ geq 3.5 \ ell+2 $ with $ s+s+s+s+s+t =χ（g）+1 $ $ $（g） $χ（g [s]）\ geq s $和$χ（g [t]）\ geq t+\ ell $。特别是，当$ \ ell = 1 $时，我们只能为任何$ s，t \ geq4 $获得相同的结果。当$ \ ell = 0 $时，Erdős-LovászTihany的猜想是一种特殊情况。
In this paper, we prove an enhanced version of the Erdős-Lovász Tihany Conjecture for line graphs of multigraphs. That is, for every graph $G$ whose chromatic number $χ(G)$ is more than its clique number $ω(G)$ and for nonnegative integer $\ell$, any two integers $s,t \geq 3.5\ell+2$ with $s+t = χ(G)+1$, there is a partition $(S,T)$ of the vertex set $V(G)$ such that $χ(G[S])\geq s$ and $χ(G[T])\geq t+\ell$. In particular, when $\ell=1$, we can obtain the same result just for any $s,t\geq4$. The Erdős-Lovász Tihany conjecture is a special case when $\ell=0$.
