论文标题
具有sublinear $ \ ell $独立编号的图表中的集团因素
Clique-factors in graphs with sublinear $\ell$-independence number
论文作者
论文摘要
给定图形$ g $和一个整数$ \ ell \ ge 2 $，我们用$α_ {\ ell}（g）$表示$ k _ {\ ell} $的最大大小 - $ v（g）$中的顶点的免费子集。 Nenadov和Pehova的最新问题要求确定最佳的最低度条件，迫使$ n $ vertex图中的集团因子$ g $带有$α_ {\ ell}（g）= O（g）= O（n）$，可以看作是著名的Hajnalle-szemeremeremeremeremerem themememeremerememeremerem therem themey-turán的变体。在本文中，我们发现$ n $ -vertex Graphs $ k_r $ - factors的渐近尖锐最低度阈值$ g $，$α__\ ell（g）= n^{1-o（1）} $ for All $ r \ ge \ ge \ ge \ ge \ ell \ ge 2 $。
Given a graph $G$ and an integer $\ell\ge 2$, we denote by $α_{\ell}(G)$ the maximum size of a $K_{\ell}$-free subset of vertices in $V(G)$. A recent question of Nenadov and Pehova asks for determining the best possible minimum degree conditions forcing clique-factors in $n$-vertex graphs $G$ with $α_{\ell}(G) = o(n)$, which can be seen as a Ramsey--Turán variant of the celebrated Hajnal--Szemerédi theorem. In this paper we find the asymptotical sharp minimum degree threshold for $K_r$-factors in $n$-vertex graphs $G$ with $α_\ell(G)=n^{1-o(1)}$ for all $r\ge \ell\ge 2$.
