An Alternative Proof of Lovász’s Cathedral Theorem
نویسنده
چکیده
A graph G with a perfect matching is called saturated if G + e has more perfect matchings than G for any edge e that is not in G. Lovász gave a characterization of the saturated graphs called the cathedral theorem, with some applications to the enumeration problem of perfect matchings, and later Szigeti gave another proof. In this paper, we give a new proof with our preceding works which revealed canonical structures of general graphs with perfect matchings. Here, the cathedral theorem is derived in quite a natural way, providing more refined or generalized properties. Moreover, the new proof shows that it can be proved without using the Gallai-Edmonds structure theorem.
منابع مشابه
The Third Proof of Lovász's Cathedral Theorem
This paper is on matching theory. A graph with perfect matching is called saturated if any addition of one complement edge creates a new perfect matching. Lovász gave a characterization of the saturated graphs called the cathedral theorem, and later Szigeti gave another proof. In this paper, we gave a new proof with our preceding works, which revealed the canonical structure of general graph wi...
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