UEFA's Champions League draw creates unfair clusters; a Cayley graph fixes it

UEFA's new league-phase format for its continental competitions inadvertently creates tight clusters of teams that play each other far more often than intended, as seen in the 2025-26 Champions League draw where five teams (Napoli, Benfica, Chelsea, Ajax, Qarabağ) are scheduled to play each other 9 of 10 possible matchups. A mathematician proposes using a specific symmetric graph structure (a Cayley graph) to eliminate this clustering problem, which would require only minor adjustments to UEFA's country-eligibility rules to implement across all competitions.