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On the uniqueness of perfect matchings in bipartite graphs. (English) Zbl 0861.05050

Summary: We give two new proofs of a characterization of the bipartite graphs that have a unique perfect matching, in terms of their adjacency matrices. One of them is based on polyhedral combinatorics while the other one makes use of a result pertaining to the theory of permanents.

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A15 Determinants, permanents, traces, other special matrix functions
05C75 Structural characterization of families of graphs
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