长洞和反洞的Erdens-Hajnal猜想
The Erdős-Hajnal Conjecture for Long Holes and Anti-holes
摘要：
Erdés和Hajnal证明了，对于每个图$H$，存在一个常数$c_H$，使得$n$顶点上的每个图$G$，如果不包含任何$H$的诱导拷贝，都有一个大小为$n^{c_H}$的团或稳定集.证明了对每个$k$，存在$c_k>0$，使得$n$顶点上的每个图$G$不包含长度至少为$k$的圈，也不包含其补图，且包含大小为$n^{c_k}$的团或稳定集.
英文摘要：
Erdős and Hajnal conjectured that, for every graph $H$, there exists a constant $c_H$ such that every graph $G$ on $n$ vertices which does not contain any induced copy of $H$ has a clique or a stable set of size $n^{c_H}$. We prove that for every $k$, there exists $c_k>0$ such that every graph $G$ on $n$ vertices not inducing a cycle of length at least $k$ nor its complement contains a clique or a stable set of size $n^{c_k}$.
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。
