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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]].\nA matching in $G$ is a set $M$ of edges of $G$ such that no two distinct edges of $M$ have a common end.\n\n## Remarks\n\nA vertex is matched if it is an end of an edge of $M$. Otherwise it is unmatched.\nA maximal matching is not contained in a larger matching. A maximum matching has the largest number of edges, the matching number $\\nu(G)$.\nEvery maximum matching is maximal, but the converse is false: in the [[path graph|075WR6W3Y3]] $P_4$, the middle edge alone is a maximal matching.\n\n## Explanations\n\n### L1 human\n\nA matching pairs some vertices along edges, and no vertex is in two pairs.\nFor example, it can pair workers with jobs that they can do, one job per worker.\n",
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