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  "body": "\n## Summary\n\nTreewidth is a number that measures how close a graph is to a [[tree|0MJ0JS72DZ]].\nIt is defined through tree decompositions, which arrange overlapping sets of vertices along a tree.\nForests have treewidth at most $1$, and the complete graph $K_n$ has treewidth $n - 1$.\nTreewidth is central in the theory of [[graph minors|VYQ32ZBPEE]].\nMany problems that are hard in general can be solved efficiently on graphs of bounded treewidth.\n\n## Explanations\n\n### L1 human\n\nA tree is easy to handle because removing any vertex that is not a leaf splits it into separate pieces.\nA graph of small treewidth has the same property in a fuzzy way.\nIt can be cut into pieces by removing small sets of vertices, again and again, in a tree-like pattern.\nFor example, a cycle is not a tree, but it has treewidth $2$, so it is almost as simple as a tree.\nA large square grid has large treewidth, because no small set of vertices splits it into small pieces.\n",
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