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Random Tournaments Are Asymptotically Almost Surely Link-irregular

  • Lily Zhang
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Abstract

Bastien and Khormali (2025) conjectured that a nontrivial link-irregular tournament with n vertices exists if and only if n ≥ 6. Their work establishes the conjecture for n ≤ 100. We present a probabilistic argument for the existence of link-irregular tournaments with n vertices when n ≥ 9 to resolve the conjecture. In fact, we show that a random tournament is asymptotically almost surely link-irregular.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026random,
  title = {{Random Tournaments Are Asymptotically Almost Surely Link-irregular}},
  author = {Lily Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24631},
  eprint = {2610.24631},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24631},
}
RIS
TY  - UNPB
TI  - Random Tournaments Are Asymptotically Almost Surely Link-irregular
AU  - Lily Zhang
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24631
UR  - https://arxiv.org/abs/2610.24631
AB  - Bastien and Khormali (2025) conjectured that a nontrivial link-irregular tournament with n vertices exists if and only if n ≥ 6. Their work establishes the conjecture for n ≤ 100. We present a probabilistic argument for the existence of link-irregular tournaments with n vertices when n ≥ 9 to resolve the conjecture. In fact, we show that a random tournament is asymptotically almost surely link-irregular.
ER  -