{
  "$type": "site.standard.document",
  "bskyPostRef": {
    "cid": "bafyreiborhayysy6ko6mcljvy574z6kzfdfa4a2osc4vdr6wdw6a42e75y",
    "uri": "at://did:plc:4rgrdigiftglskeax4wvmsev/app.bsky.feed.post/3mlnlxfejvgi2"
  },
  "coverImage": {
    "$type": "blob",
    "ref": {
      "$link": "bafkreiflo6xt7is6b2iafwghkjahlgggocme5jwjsbeuqqwcywuvjhmszm"
    },
    "mimeType": "image/png",
    "size": 24783
  },
  "path": "/abs/2605.10941v1",
  "publishedAt": "2026-05-12T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Susanna F. de Rezende",
    "David Engström",
    "Yassine Ghannane",
    "Duri Andrea Janett",
    "Artur Riazanov"
  ],
  "textContent": "**Authors:** Susanna F. de Rezende, David Engström, Yassine Ghannane, Duri Andrea Janett, Artur Riazanov\n\nWe 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.",
  "title": "Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity"
}