Multiplayer Parallel Repetition Is the Same as High-Dimensional Extremal Combinatorics
Computational Complexity
2025-10-30 v1 Combinatorics
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 -player games, and establishes new connections to problems in combinatorics. We believe that these connections may help future progress in both fields.
Keywords
Cite
@article{arxiv.2510.24910,
title = {Multiplayer Parallel Repetition Is the Same as High-Dimensional Extremal Combinatorics},
author = {Kunal Mittal},
journal= {arXiv preprint arXiv:2510.24910},
year = {2025}
}