标题： 竞赛图的循环子集 显示英文标题

标题： Cyclic subsets of tournaments

摘要： 设$G$是一个狄拉克图，令$S$是$G$的一个顶点子集，以均匀随机的方式选择。 诱导子图$G[S]$成为哈密顿图的可能性有多大？ 这个问题由埃德罗斯和福德里于1996年提出，最近在图的设定下由德拉加尼奇、基夫什和穆耶瑟解决了。 在本文中，我们研究了类似的问题对于竞赛图——如果$T$是一个最小度较高的竞赛图，那么随机诱导的$T$的子竞赛图成为哈密顿图的可能性有多大？ 我们证明了该概率的最优界限，并将结果扩展到子集不是以均匀随机方式采样，而是根据$p$-偏倚测度采样的情况。 显示英文摘要

摘要： Let $G$ be a Dirac graph, and let $S$ be a vertex subset of $G$, chosen uniformly at random. How likely is the induced subgraph $G[S]$ to be Hamiltonian? This question, proposed by Erd\H{o}s and Faudree in 1996, was recently resolved by Dragani\'c, Keevash and M\"uyesser, in the setting of graphs. In this paper, we study a similar question for tournaments -- if $T$ is a tournament of high minimum degree, how likely is it for a random induced subtournament of $T$ to be Hamiltonian? We prove an optimal bound on this probability, and extend the results to the regime where the subset is not sampled uniformly at random, but according to a $p$-biased measure.