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  "body": "\n## Summary\n\nIn a graph with a matching, an alternating path is a path whose edges alternate between matched and unmatched edges. An alternating cycle is, similarly, a cycle whose edges alternate between matched and unmatched edges. An augmenting path is an alternating path that starts and ends at unsaturated vertices. A larger matching can be found as the [[symmetric difference|0ME21QN125]] of the matching and the augmenting path; a matching is maximum if and only if it has no augmenting path.\n",
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