{
  "aliases": [
    "preclude"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn graph theory, a branch of mathematics, the **matching preclusion number** of a graph $G$, denoted $\\mathrm{mp}(G)$, is the minimum number of edges whose deletion results in the elimination of all [[perfect matchings|05ZPH8KF9K]] or near-perfect matchings (matchings that cover all but one vertex in a graph with an odd number of vertices). Matching preclusion measures the quality of a graph as a communications network topology for distributed algorithms that require each node of the distributed system to be matched with a neighboring partner node.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "aliases": [
      "preclude"
    ],
    "inventory": [
      "PJ2TW38TB7"
    ],
    "kind": "concept",
    "name": "Matching preclusion",
    "same_as": {
      "wikidata": "Q17135100",
      "wikipedia": "Matching preclusion"
    },
    "sources": [
      {
        "locator": "Matching preclusion",
        "mention": "wikipedia://en/27970912",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:27970912@r1322814211"
      }
    ],
    "tag": "SSC5WGWKW9"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/SSC5WGWKW9/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/SSC5WGWKW9.md",
  "msc": null,
  "name": "Matching preclusion",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/SSC/SSC5WGWKW9.md",
  "status": null,
  "tag": "SSC5WGWKW9",
  "uri": "m2://SSC5WGWKW9",
  "url": "https://math2.tamnd.com/wiki/matching-preclusion/",
  "writing": {
    "tag": "SSC5WGWKW9",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}