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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]].\nA vertex cover of $G$ is a set $S$ of vertices of $G$ that contains at least one end of each edge.\n\n## Remarks\n\nA set $S$ is a vertex cover if and only if its complement is an [[independent set|0KZJ82WEPP]].\nFor the [[complete bipartite graph|0V0GC7BQAN]] $K_{m,n}$, the least size of a vertex cover is $\\min\\{m, n\\}$.\nEach vertex of a cover meets at most one edge of a [[matching|0Z87BHAFTB]]. Thus every vertex cover has at least as many vertices as any matching has edges.\n\n## Explanations\n\n### L1 human\n\nA vertex cover is a set of vertices that touches every edge.\nThink of guards at crossings: each street must have a guard at one of its two ends.\n",
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