{
  "id": "1503.02885",
  "version": "v1",
  "published": "2015-03-10T12:42:12.000Z",
  "updated": "2015-03-10T12:42:12.000Z",
  "title": "A remark on the Tournament game",
  "authors": [
    "Dennis Clemens",
    "Mirjana Mikalački"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the Maker-Breaker tournament game played on the edge set of a given graph $G$. Two players, Maker and Breaker claim unclaimed edges of $G$ in turns, and Maker wins if by the end of the game she claims all the edges of a pre-defined goal tournament. Given a tournament $T_k$ on $k$ vertices, we determine the threshold bias for the $(1:b)$ $T_k$-tournament game on $K_n$. We also look at the $(1:1)$ $T_k$-tournament game played on the edge set of a random graph ${\\mathcal{G}_{n,p}}$ and determine the threshold probability for Maker's win. We compare these games with the clique game and discuss whether a random graph intuition is satisfied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-10T12:42:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "edge set",
      "breaker claim unclaimed edges",
      "random graph intuition",
      "maker-breaker tournament game",
      "maker wins"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150302885C"
    }
  }
}