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A New Upper Bound for 7-Universal Tournaments

  • Harshit Verma
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Abstract

We give an explicit tournament on 14 vertices containing every 7-vertex tournament as an induced sub-tournament, and verify this property by exhaustive computation. This improves the previously known upper bound of 15. Together with the known lower bound, it follows that the minimum order of a 7-universal tournament is either 13 or 14.

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Cite

BibTeXRIS
BibTeX
@misc{verma2026upper,
  title = {{A New Upper Bound for 7-Universal Tournaments}},
  author = {Harshit Verma},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06891},
  eprint = {2610.06891},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06891},
}
RIS
TY  - UNPB
TI  - A New Upper Bound for 7-Universal Tournaments
AU  - Harshit Verma
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.06891
UR  - https://arxiv.org/abs/2610.06891
AB  - We give an explicit tournament on 14 vertices containing every 7-vertex tournament as an induced sub-tournament, and verify this property by exhaustive computation. This improves the previously known upper bound of 15. Together with the known lower bound, it follows that the minimum order of a 7-universal tournament is either 13 or 14.
ER  -