A short proof of the Berge-Tutte Formula and the Gallai-Edmonds Structure Theorem

@article{West2011ASP,
  title={A short proof of the Berge-Tutte Formula and the Gallai-Edmonds Structure Theorem},
  author={Douglas B. West},
  journal={Eur. J. Comb.},
  year={2011},
  volume={32},
  pages={674-676}
}
We present a short proof of the Berge–Tutte Formula and the Gallai–Edmonds Structure Theorem from Hall’s Theorem. The fundamental theorems on matchings in graphs have been proved in many ways. The most famous of these results is Hall’s Theorem [6], characterizing when a bipartite graph has a matching that covers one partite set. Anderson [1] used Hall’s Theorem to prove Tutte’s 1Factor Theorem [9], characterizing when a graph has a perfect matching. Berge [2] extended Tutte’s 1-Factor Theorem… CONTINUE READING

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