标题： 无限多的反例对洛瓦斯的一个猜想 显示英文标题

标题： Infinitely many counterexamples to a conjecture of Lovász

摘要： 受Ryser著名的猜想的启发，该猜想将最大匹配与最小顶点覆盖联系起来，适用于$r$-分图$r$-一致超图，Lovász提出了一个更强的猜想。它指出，总能通过移除$r-1$个顶点来减少匹配数。这个猜想最近被Clow、Haxell和Mohar用阶数为$102$的$3$-正则图的线图所否定，针对$r=3$的情况。 在此基础上，我们描述了一个基于广义彼得森图的简单无限反例族，用于情况$r=3$，并给出了$r=4$的具体反例。 显示英文摘要

摘要： Motivated by the well-known conjecture of Ryser which relates maximum matchings to minimum vertex covers in $r$-partite $r$-uniform hypergraphs, Lov\'asz formulated a stronger conjecture. It states that one can always reduce the matching number by removing $r-1$ vertices. This conjecture was very recently disproven for $r=3$ by Clow, Haxell, and Mohar using the line graph of a $3$-regular graph of order $102$. Building on this, we describe a simple infinite family of counterexamples based on generalized Petersen graphs for the case $r=3$ and give specific counterexamples for $r=4$.