This article is cited in 2 papers

Inert matrices and matchings in partially oriented trees

V. A. Kolmykov


Abstract: We study inert matrices which remain degenerate or non-degenerate under any replacement of their non-zero elements by other non-zero numbers. In partially oriented graphs, we consider non-oriented matchings. We discuss a quantum model which fit these matchings. We prove that both perfect and imperfect oriented trees (that is, possessing and not possessing a perfect matching) may be obtained from the elementary ones with the use of some operations, that is, the set of the perfect trees and the set of the imperfect trees are free finitely generated algebraic structures.

UDC: 519.17

Received: 13.12.2001
Revised: 08.10.2002

DOI: 10.4213/dm220

 English version: Discrete Mathematics and Applications, 2003, 13:6, 607–612

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