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  "body": "\n## Summary\n\nIn graph theory, a **priority matching** (also called: **maximum priority matching**) is a [[matching|0MJ04A50QW]] that maximizes the number of high-priority vertices that participate in the matching. Formally, we are given a [[graph|00C0BR7D7H]] $G = (V, E)$, and a partition of the vertex-set $V$ into some $k$ subsets, $V_{1}, \\ldots, V_{k}$, called *priority classes*. A priority matching is a matching that, among all possible matchings, saturates the largest number of vertices from $V_{1}$; subject to this, it saturates the largest number of vertices from $V_{2}$; subject to this, it saturates the largest number of vertices from $V_{3}$; and so on.\n",
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