AI 中文总结
研究二分图中匹配与共匹配，对于具有强埃尔德什 - 哈伊纳尔性质的二分图类，在禁止森林及其二分补图的基础上，给出了限制为匹配时\(\varepsilon\)的定量界。
AI 中文摘要
如果存在\(\varepsilon>0\)，使得某类二分图\(((A,B),E)\)中的每个图都包含一个诱导子图，其部分\(X\subseteq A\)，\(Y\subseteq B\)，满足\(|X|\geq\varepsilon|A|\)且\(|Y|\geq\varepsilon|B|\)，则称该类二分图具有强埃尔德什 - 哈伊纳尔性质。Scott、Seymour和Spirkl证明禁止森林及其二分补图就足够了。本文在限制为匹配时给出了\(\varepsilon\)的定量界。
英文摘要
A class of bipartite graphs is said to have the strong Erdős-Hajnal property if there exists $\varepsilon > 0$ such that every graph $((A, B), E)$ in the class contains a complete or empty induced subgraph with parts $X \subseteq A$, $Y \subseteq B$ where $|X| \ge \varepsilon|A|$ and $|Y| \ge \varepsilon|B|$. Scott, Seymour and Spirkl proved that it is enough to forbid a forest and the bipartite complement of a forest. In this paper, we provide quantitative bounds on $\varepsilon$ when we restrict to matchings.
