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An application of the structural theory of acyclic skew-symmetric graphs. (Russian, English) Zbl 1164.05056

Vestn. Mosk. Univ., Ser. I 2007, No. 2, 65-66 (2007); translation in Mosc. Univ. Math. Bull. 62, No. 2, 85-86 (2007).
It is known (see [L. Lovasz and M. Plummer, “Applied problems of graph theory. The theory of pair combination in mathematics, physics and chemistry”, Mir, Moscow (1998)]) that if in the non-oriented graph \(G\) a unique perfect pair combination \(M\) exists then at least one of the bridges \(C\) is contained in \(M\). In the present paper an alternative simple proof of this assertion is proposed. It is based on the structural theory of acyclic skew-symmetric graphs developed by the author.

MSC:

05C75 Structural characterization of families of graphs
05C90 Applications of graph theory