{
  "aliases": [
    "aanderaa-rosenberg-conjecture",
    "evasiveness",
    "evasiveness-conjecture"
  ],
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  "body": "\n## Statement\n\nIn theoretical computer science, the **Aanderaa–Karp–Rosenberg conjecture** (also known as the **Aanderaa–Rosenberg conjecture** or the **evasiveness conjecture**) is a group of related conjectures about the number of questions of the form \"Is there an edge between vertex $u$ and vertex $v$?\" that have to be answered to determine whether or not an undirected graph has a particular property such as [[planarity|029JQEK15B]] or [[bipartiteness|07DVHJ8N0A]]. They are named after Stål Aanderaa, Richard M. Karp, and Arnold L. Rosenberg. According to the conjecture, for a wide class of properties, no algorithm can guarantee that it will be able to skip any questions: any algorithm for determining whether the graph has the property, no matter how clever, might need to examine every pair of vertices before it can give its answer. A property satisfying this conjecture is called evasive.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
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      "wikidata": "Q4661558",
      "wikipedia": "Aanderaa–Karp–Rosenberg conjecture"
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        "locator": "Aanderaa–Karp–Rosenberg conjecture",
        "mention": "wikipedia://en/21681084",
        "note": "adopted",
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        "wikipedia": "en:21681084@r1375125283"
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    "tag": "Q74KEMA8TE"
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  "markdown": "https://math2.tamnd.com/node/Q74KEMA8TE.md",
  "msc": null,
  "name": "Aanderaa–Karp–Rosenberg conjecture",
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  "source": "https://github.com/tamnd/math2/blob/main/nodes/Q74/Q74KEMA8TE.md",
  "status": null,
  "tag": "Q74KEMA8TE",
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  "url": "https://math2.tamnd.com/wiki/aanderaa-karp-rosenberg-conjecture/",
  "writing": {
    "tag": "Q74KEMA8TE",
    "kind": "conjecture",
    "level": "W0",
    "next": [
      {
        "what": "edge uses out",
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}