A Cayley graph could fix UEFA's unfair Champions League draw
UEFA's Champions League draw creates unfair clusters; a Cayley graph fixes it
The 2025-26 Champions League draw produced a tight cluster: Napoli, Benfica, Chelsea, Ajax, and Qarabağ play 9 of their 10 possible pairings, hurting their joint chances of advancing. This pattern recurs every season in UEFA's new league-phase format. The author shows how a symmetric graph on 36 vertices—a Cayley graph—can eliminate such dense clusters by design, requiring only a small tweak to the country rule for UCL/UEL and none for UECL.
The point isn’t that this specific draw was cursed; it’s somewhat above average in cluster density (roughly top 20% of comparable random draws we simulated), not statistically extreme. It’s that the format allows this.