Show that the problem of finding the minimum vertex cover in a bipartite graph reduces to finding a maximum flow. Describe the reduction in a precise and concise way.
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Call the two partitions of the nodes $A$ and $B$. Add two new nodes, a source $s$ and a sink $t$. Connect the start node to all nodes in $A$ with an edge with max capacity of one. Connect all the nodes in $B$ to the sink with edges with a max capacity of one. And lastly give all the original edges in the graph a max capacity of one. Now finding the max flow from $s$ to $t$ will find the minimum vertex cover.
For each edge $(u,v)$ included in the max-flow, the nodes $u$ and $v$ will be a part of the minimum vertex cover.
Draw this and you will understand.