Abstract
A graph G is said to possess a perfect matching if there is a subgraph of G consisting of disjoint edges which together cover all the vertices of G. Clearly G must then have an even number of vertices. A necessary and sufficient condition for G to possess a perfect matching was obtained by Tutte (3). If S is any set of vertices of G, let p(S) denote the number of components of the graph G – S with an odd number of vertices. Then the conditionis both necessary and sufficient for the existence of a perfect matching. A simple proof of this result is given in (1).
Publisher
Cambridge University Press (CUP)
Reference4 articles.
1. The Factorization of Linear Graphs
2. (4) Woodall D. R. , The melting point of a graph, and its Anderson number (to appear).
3. Perfect matchings of a graph
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6 articles.
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