{
  "id": "ramsey-4-4",
  "family": "ramsey",
  "kind": "practice",
  "title": "Ramsey number R(4,4): a graph with no 4-clique and no 4-independent set",
  "params": {
    "s": 4,
    "t": 4
  },
  "record": "17",
  "record_meaning": "R(4,4) = 18, so 17 vertices is the most possible",
  "record_from": "listed: Radziszowski, Small Ramsey Numbers (dynamic survey DS1), read 2026-11-04",
  "exact": true,
  "source_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS1",
  "keeper": "Radziszowski's dynamic survey of small Ramsey numbers",
  "url": "/v1/science/math/problems/ramsey-4-4",
  "source": "Radziszowski, Small Ramsey Numbers (dynamic survey DS1)",
  "as_of": "2026-11-04",
  "how_to_submit": "construction: {n, edges: [[i, j], ...]} with vertices 0 to n-1, or {graph6: \"...\"}. The graph must have no s vertices all joined and no t vertices with no edges among them. Score = n, which proves R(s,t) ≥ n+1. Up to 160 vertices.",
  "example_construction": {
    "n": 5,
    "edges": [
      [
        0,
        1
      ],
      [
        1,
        2
      ],
      [
        2,
        3
      ],
      [
        3,
        4
      ],
      [
        4,
        0
      ]
    ]
  },
  "leaderboard": []
}