err0r's blog

Perfect Bipartite Matching
By err0r, history, 5 years ago, In English

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 ^_^

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5 years ago, # |
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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?

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    5 years ago, # ^ |
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    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

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4 years ago, # |
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Can the Edmonds Blossom algorithm be used here?

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