{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "1FFTQW1B1X"
    },
    {
      "field": "defines",
      "target": "7Z0QZP0FC0"
    }
  ],
  "body": "\n## Summary\n\nA minor of a [[matroid|PX31ZNYS3Z]] is a matroid obtained from it by deleting some elements and contracting others.\nDeletion and contraction generalize the deletion and contraction of edges of a graph, and they are exchanged by [[matroid duality|6QF83CFK2G]].\nMany classes of matroids are closed under minors and are characterized by a list of excluded minors.\nThis parallels the role of [[graph minors|VYQ32ZBPEE]] for classes of graphs.\n\n## Explanations\n\n### L1 human\n\nDeleting an element just throws it away together with every independent set that uses it.\nContracting an element that is not a loop means treating it as already chosen: a set counts as independent when it stays independent after adding that element.\nFor a graph, deletion removes an edge and contraction shrinks an edge to a point.\nA minor is anything you can reach by doing these two operations several times.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "05B35"
    ],
    "name": "Matroid minor",
    "same_as": {
      "wikidata": "Q17086290",
      "wikipedia": "Matroid minor"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Matroid_minor"
      }
    ],
    "tag": "4WCYBSH1P6"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/4WCYBSH1P6/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/4WCYBSH1P6.md",
  "msc": [
    "05B35"
  ],
  "name": "Matroid minor",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/4WC/4WCYBSH1P6.md",
  "status": null,
  "tag": "4WCYBSH1P6",
  "uri": "m2://4WCYBSH1P6",
  "url": "https://math2.tamnd.com/wiki/matroid-minor/",
  "writing": {
    "tag": "4WCYBSH1P6",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}