A Theorem on the Principal Structure for Independent Matchings

This paper defines the notion of principal structure for independent matchings as a particular instance of the principal structure of submodular systems due to Fujishige. A theorem which reveals the relationship between the principal structure and the principal partition is established. Previously known results on bipartite matchings and layered mixed matrices can be understood as special cases of this result.

[1]  Satoru Iwata,et al.  Horizontal Principal Structure of Layered Mixed Matrices: Decomposition of Discrete Systems by Design-Variable Selections , 1996, SIAM J. Discret. Math..

[2]  Martin Grötschel,et al.  Mathematical Programming The State of the Art, XIth International Symposium on Mathematical Programming, Bonn, Germany, August 23-27, 1982 , 1983, ISMP.

[3]  A. Recski.  Matroid theory and its applications in electric network theory and in statics , 1989 .

[4]  K. Murota.  Systems Analysis by Graphs and Matroids: Structural Solvability and Controllability , 1987 .

[5]  Kazuo Murota,et al.  Combinatorial canonical form of layered mixed matrices and its application to block-triangularization of systems of linear/nonlinear equations , 1987 .

[6]  Satoru Fujishige,et al.  Submodular functions and optimization , 1991 .

[7]  M. Iri,et al.  Applications of Matroid Theory , 1982, ISMP.

[8]  Kazuo Murota,et al.  Mixed Matrices — Irreducibility and Decomposition — ⁄ , 1993 .

[9]  M. Iri,et al.  Use of matroid theory in operations research, circuits and systems theory , 1981 .

[10]  W. Pulleyblank.  Progress in combinatorial optimization , 1985 .

[11]  Masao Iri,et al.  Structural Theory for the Combinatorial Systems Characterized by Submodular Functions , 1984 .

[12]  Satoru Fujishige,et al.  Principal structures of submodular systems , 1980, Discret. Appl. Math..

[13]  Kazuo Murota,et al.  Principal structure of layered mixed matrices , 1990, Discret. Appl. Math..

[14]  S. T. McCormick,et al.  A combinatorial approach to some sparse matrix problems , 1983 .