Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity

Susanna F. de Rezende; David Engström; Yassine Ghannane; Duri Andrea Janett; Artur Riazanov

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arXiv · 2605.10941

Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity

Susanna F. de Rezende·David Engström·Yassine Ghannane·Duri Andrea Janett·Artur Riazanov

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Abstract

We study the average-case hardness of establishing that a graph does not have a large clique in both proof and communication complexity. We show exponential lower bounds on the length of cutting planes and bounded-depth resolution over parities refutations of the binary encoding of clique formulas on randomly sampled dense graphs. Moreover, we show that the randomized communication complexity of finding a falsified clause in these formulas is polynomial.

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Susanna F. de Rezende, David Engström, Yassine Ghannane, Duri Andrea Janett, Artur Riazanov. 2026-05-11. Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity. https://arxiv.org/abs/2605.10941

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