Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2605.10941

Authors: de Rezende, Susanna F., Engström, David, Ghannane, Yassine, Janett, Duri Andrea, Riazanov, Artur

Institutions: Lund University, University of Copenhagen, École Polytechnique Fédérale de Lausanne

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7160936019

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