Kőnig's theorem is a fundamental result in graph theory, specifically in the area of bipartite graphs and matching. It states that in any bipartite graph, the size of the maximum matching (the largest set of edges that do not share a vertex) is equal to the size of the minimum vertex cover (the smallest set of vertices such that every edge in the graph is incident to at least one vertex from this set).
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In a finite bipartite graph, the maximum size of a matching equals the minimum size of a vertex cover. It follows by representing matching as an integral flow and vertex covers as finite-capacity cuts.