Locally finite perturbation conjecture for non-transitive tournaments

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Let TT 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 TT is not transitive, then there exists a countably infinite TT-free tournament STS_T such that every locally finite perturbation of STS_T has an induced copy of TT. The requirement that TT 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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