ABSTRACT Let be a Dirac graph, and let be a vertex subset of , chosen uniformly at random. How likely is the induced subgraph to be Hamiltonian? This question, proposed by Erdős and Faudree in 1996, was recently resolved by Draganić, Keevash, and Müyesser, in the setting of graphs. In this paper, we study a similar question for tournaments: If is a tournament of high minimum degree, how likely is it for a random induced subtournament of 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 ‐biased measure.
Hunter et al. (2026) studied this question.