{
  "id": "1503.03855",
  "version": "v1",
  "published": "2015-03-12T19:42:02.000Z",
  "updated": "2015-03-12T19:42:02.000Z",
  "title": "Hypergraph Ramsey numbers: tight cycles versus cliques",
  "authors": [
    "Dhruv Mubayi",
    "Vojtech Rodl"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For $s \\ge 4$, the 3-uniform tight cycle $C^3_s$ has vertex set corresponding to $s$ distinct points on a circle and edge set given by the $s$ cyclic intervals of three consecutive points. For fixed $s \\ge 4$ and $s \\not\\equiv 0$ (mod 3) we prove that there are positive constants $a$ and $b$ with $$2^{at}<r(C^3_s, K^3_t)<2^{bt^2\\log t}.$$ The lower bound is obtained via a probabilistic construction. The upper bound for $s>5$ is proved by using supersaturation and the known upper bound for $r(K_4^{3}, K_t^3)$, while for $s=5$ it follows from a new upper bound for $r(K_5^{3-}, K_t^3)$ that we develop.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-12T19:42:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10"
    ],
    "keywords": [
      "hypergraph ramsey numbers",
      "tight cycle",
      "upper bound",
      "distinct points",
      "edge set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}