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Math Help - Graph Theory problem

  1. #1
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    Graph Theory problem

    Let G = (A \cup B, E) be a simple bipartite graph, such that |A| = |B| = n and |E| = e and such that for every vertex v in the graph, deg(v) = 2k+1 for some k \in \mathbb{N}

    Also, there is a closed path (the last vertex is the same as the first) of length e+n that goes over every vertex in G at least once.

    Prove that there is a perfect matching on G.

    Pretty much at a loss on how I should do this. Any help is welcome.

    I most likely need to use either Konig's theorem, or Hall's to solve this, but as I said I couldn't see where I could apply them.
    Last edited by Defunkt; October 10th 2009 at 03:03 AM.
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