Koning’s theorem states that the cardinality of the maximum matching in a bipartite graph is equal to the size of its minimum vertex cover.
Wikipedia states that there is an equivalent version of the theorem for weighted graphs as well. I tried searching in a lot of places but could not find this theorem.
To be more specific, I want to know what is the equivalent version of Konig’s theorem in the case of Minimum Weight Vertex Cover in Bipartite Graphs where each vertex $ v \in G$ is assigned a weight $ w_v$ and the task is to find a vertex cover of the minimum possible weight.
If the equivalence is just the maximum weighted matching in $ G$ , what are the weights of the edges in this graph? Because as far as I understand, we have only assigned weights to the vertices of the graph $ G$ .
Thank you for your time 🙂
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