What question did this study set out to answer?

This research explores the likelihood of a random induced subtournament being Hamiltonian in Dirac graphs.

March 10, 2026Open Access

Cyclic Subsets of Tournaments

Puntos clave

This research explores the likelihood of a random induced subtournament being Hamiltonian in Dirac graphs.
Analyzed tournaments with high minimum degree.
Investigated random vertex subset selection methods.
Determined probability bounds for induced subtournaments.
Provided an optimal bound on the probability of Hamiltonian induced subtournaments.
Extended findings to non-uniformly sampled vertex subsets.

Resumen

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.

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