论文标题
$ h $ - 图表中的独立编号很小的图形
$H$-factors in graphs with small independence number
论文作者
论文摘要
令$ h $为$ h $ vertex图。 $ h $的顶点Arboricity $ ar（h）$是最小整数$ r $，因此可以将$ v（h）$划分为$ r $零件，每个零件以$ h $诱导森林。我们表明，对于H \ Mathbb {n} $中的足够大的$ n \，每个$ n $ vertex graph $ g $带有$Δ（g）\ geq \ geq \ max \ max \ left \ left \ {\ left（1- \ frac {2} \ left（\ frac {1} {2}+o（1）\ right）n \ right \} $和$α（g）= o（n）$包含$ h $ -factor，其中$ f（h）= 2ar（h）= 2ar（h）$或$ 2ar（h）$ 2ar（h）-1 $。 The result can be viewed an analogue of the Alon--Yuster theorem \cite{MR1376050} in Ramsey--Turán theory, which generalises the results of Balogh--Molla--Sharifzadeh~\cite{MR3570984} and Knierm--Su~\cite{MR4193066} on clique factors.特别是，对于无限的图形$ h $而不是集团，程度条件在渐近上是渐近的。
Let $H$ be an $h$-vertex graph. The vertex arboricity $ar(H)$ of $H$ is the least integer $r$ such that $V(H)$ can be partitioned into $r$ parts and each part induces a forest in $H$. We show that for sufficiently large $n\in h\mathbb{N}$, every $n$-vertex graph $G$ with $δ(G)\geq \max\left\{\left(1-\frac{2}{f(H)}+o(1)\right)n, \left(\frac{1}{2}+o(1)\right)n\right\}$ and $α(G)=o(n)$ contains an $H$-factor, where $f(H)=2ar(H)$ or $2ar(H)-1$. The result can be viewed an analogue of the Alon--Yuster theorem \cite{MR1376050} in Ramsey--Turán theory, which generalises the results of Balogh--Molla--Sharifzadeh~\cite{MR3570984} and Knierm--Su~\cite{MR4193066} on clique factors. In particular the degree conditions are asymptotically sharp for infinitely many graphs $H$ which are not cliques.
