{
  "aliases": null,
  "backlinks": [
    {
      "field": "proves",
      "target": "4Y6ZD17WNZ"
    }
  ],
  "body": "\n## Statement\n\nA natural generalization of the graph removal lemma is to consider [[induced subgraphs|0EREPBVG2G]]. In property testing, it is often useful to consider how far a graph is from being induced $H$-free. A graph $G$ is considered to contain an induced subgraph $H$ if there is an injective map $f: V(H) \\rightarrow V(G)$ such that $(f(u),f(v))$ is an edge of $G$ if and only if $(u,v)$ is an edge of $H$. Notice that non-edges are considered as well. $G$ is induced $H$-free if there is no induced subgraph $G$. We define $G$ as $\\epsilon$-far from being induced $H$-free if we cannot add or delete $\\epsilon n^2$ edges to make $G$ induced $H$-free.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "VMZS5XS05S"
    ],
    "kind": "statement",
    "name": "Induced Graph Removal Lemma",
    "role": "lemma",
    "sources": [
      {
        "locator": "Graph removal lemma, section Induced Graph Removal Lemma",
        "mention": "wikipedia://en/59842040#9ICI",
        "note": "adopted",
        "sections": [
          "Statement"
        ],
        "wikipedia": "en:59842040@r1360690218"
      }
    ],
    "tag": "YWZQFCJB2K"
  },
  "kind": "statement",
  "link": "https://math2.tamnd.com/node/YWZQFCJB2K/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/YWZQFCJB2K.md",
  "msc": null,
  "name": "Induced Graph Removal Lemma",
  "prov": null,
  "role": "lemma",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/YWZ/YWZQFCJB2K.md",
  "status": null,
  "tag": "YWZQFCJB2K",
  "uri": "m2://YWZQFCJB2K",
  "url": "https://math2.tamnd.com/wiki/induced-graph-removal-lemma/",
  "writing": {
    "tag": "YWZQFCJB2K",
    "kind": "statement",
    "level": "W0",
    "next": [
      {
        "what": "edge uses out",
        "note": "each definition that the statement needs",
        "have": 0,
        "want": 1
      }
    ]
  }
}