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Answers for “为什么将匹配形式化为从女孩到男孩的沿边双射?”

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The bipartite matching problem requires assigning each object on the left side to a distinct and compatible object on the right side. Formally, it seeks a bijection from the left set to the right set that follows the edges of the graph.

Conditions: Given a bipartite graph.; Edges represent allowable pairings.; Goal is to establish a one-to-one pairing for the left vertices.

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A bipartite graph is a graph whose vertices are divided into two disjoint sets, called left vertices and right vertices. Every vertex belongs to exactly one side, and every edge connects a left vertex to a right vertex.

Conditions: The graph is a simple graph.; The vertex set is partitioned into two disjoint subsets.; The two endpoints of each edge belong to opposite sides.