Locally finite perturbation conjecture for non-transitive tournaments
Let be a finite tournament. A locally finite perturbation of a tournament is obtained by changing the direction of arcs in a locally finite set. Tournament perturbation conjecture. If is not transitive, then there exists a countably infinite -free tournament such that every locally finite perturbation of has an induced copy of . The requirement that is not transitive is necessary because every sufficiently large finite tournament contains arbitrarily large transitive subtournaments; the conjecture proposes an analogue of the paper's graph result for tournaments and remains open.
References
Primary source
Marthe Bonamy, Carla Groenland, Tom Johnston, Natasha Morrison and Alex Scott, “Infinite induced-saturated graphs”, arXiv:2506.08810 (2025).
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