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How can i find maximum perfect matching in a bipartite graph?
it can be a a sub-graph of main bipartite graph? sub-graph contains a subset of vertex from left side and a subset of vertex from right side. if we take a vertex, each vertex that shares a edge with the selected vertex must be present in the subset of vertex too.
Thanks in Advance ^_^
Wrong solution
Just take the maximum matching and remove all unmatched vertices. proof: let's say the maximum matching is n and there is a subset with a perfect matching of m and m > n then this is a contradiction since this subset can be matched in the original graph.
Can you share the link to the problem pls?
link
sorry i think did not explain the statement properly or did not understand your solution.
in my defense i can`t remove all the unmatched vertices as there might be a edge between matched and unmatched vertices!!' for example take a graph where number of node in left side is 1 and right side is 2 and the edges are
l1->r1
l1->r2
max matching is 1. suppose chosen edge is l1 r1 but here i can`t remove r2 as there is a edge between l1 and r2
sorry misunderstood the problem
Can the Edmonds Blossom algorithm be used here?
I guess you can wait till 11th May :P