Multiplayer Parallel Repetition Is the Same as High-Dimensional Extremal Combinatorics

Kunal Mittal

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arXiv · 2510.24910

Multiplayer Parallel Repetition Is the Same as High-Dimensional Extremal Combinatorics

Kunal Mittal

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Abstract

We show equivalences between several high-dimensional problems in extremal combinatorics and parallel repetition of multiplayer (multiprover) games over large answer alphabets. This extends the forbidden-subgraph technique, previously studied by Verbitsky (Theoretical Computer Science 1996), Feige and Verbitsy (Combinatorica 2002), and H\k{a}z{\l}a , Holenstein and Rao (2016), to all $k$-player games, and establishes new connections to problems in combinatorics. We believe that these connections may help future progress in both fields.

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Kunal Mittal. 2025-10-28. Multiplayer Parallel Repetition Is the Same as High-Dimensional Extremal Combinatorics. https://arxiv.org/abs/2510.24910

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