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Universal Tournament


A universal tournament of order k, or k-universal tournament, is a tournament containing every tournament on k vertices as an induced subgraph. Write t(k) for the smallest number of vertices in such a tournament.

Verma (2026) gave an explicit tournament on 14 vertices and checked by exhaustive computation that it is 7-universal. Together with the known lower bound this gives t(7) in {13,14}, improving the previous upper bound of 15 but not determining t(7) exactly.


See also

Tournament

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References

Verma, H. "A New Upper Bound for 7-Universal Tournaments." 24 Sep 2026. https://arxiv.org/abs/2610.06891.

Cite this as:

Weisstein, Eric W. "Universal Tournament." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UniversalTournament.html

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