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arXiv · 2508.03634

Cyclic subsets of tournaments

Zach Hunter·Teng Liu·Aleksa Milojević·Benny Sudakov
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Abstract

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.

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Zach Hunter, Teng Liu, Aleksa Milojević, Benny Sudakov. 2025-08-05. Cyclic subsets of tournaments. https://arxiv.org/abs/2508.03634

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