Decomposition of Balanced Matrices

Journal of Combinatorial Theory. Series B

Volumn 77, Issue 2, 1999, Pages 292-406

  Conforti, Michele ^a   Cornuéjols, Gérard ^b   Rao, M R ^c  

^a UNIVERSITY OF PADOVA   (Italy)

^b CARNEGIE MELLON UNIVERSITY   (United States)

^c INDIAN INSTITUTE OF MANAGEMENT BANGALORE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0004712767     PISSN: 00958956     EISSN: None     Source Type: Journal    
DOI: 10.1006/jctb.1999.1932     Document Type: Article

References (31)

1. Anstee R., Farber M. Characterization of totally balanced matrices. J. Algorithms. 5:1984;215-230.
2. Berge C. Sur certains hypergraphes généralisant les graphes bipartis. Erdos P., Rényi A., Sós V. Combinatorial Theory and its Applications I. Colloq. Math. Soc. János Bolyai. 4:1970;119-133 North Holland.
3. Berge C. Balanced matrices. Math. Programming. 2:1972;19-31.
4. Berge C. Graphs and hypergraphs. 1973;North Holland.
5. Berge C. Balanced matrices and the property G. Math. Programming Study. 12:1980;163-175.
6. Berge C. Minimax theorems for normal and balanced hypergraphs. A survey. Berge C., Chvátal V. Topics on perfect graphs. Annals of Discrete Mathematics. 21:1984;3-21.
7. Berge C. Minimax relations for the partial q-colorings of a graph. Discrete Math. 74:1989;3-14.
8. Berge C., Las Vergnas M. Sur un théorème du type König pour les hypergraphes. Annals of the New York Academy of Sciences. 175:1970;32-40.
9. Camion P. Characterization of totally unimodular matrices. Proc. Amer. Math. Soc. 16:1965;1068-1073.
10. Commoner F. G. A sufficient conditions for a matrix to be totally unimodular. Networks. 3:1973;351-365.
11. Conforti M., Cornuéjols G. A decomposition theorem for balanced matrices. Kannan R., Pulleyblank W. R. Integer Programming and Combinatorial Optimization. 1990;147-169 Waterloo University Press.
12. Conforti M., Cornuéjols G., Kapoor A., Rao M. R., Vusković K. Balanced matrices. Birge J. R., Murty K. G. Mathematical Programming: State of the Art 1994. 1994;1-33 The University of Michigan Press.
13. M. Conforti, G. Cornuéjols, A. Kapoor, and, K. Vusković, Balanced 0, +1, -1 matrices, preprints, 1993.
14. Conforti M., Cornuéjols G., Kapoor A., Vusković K. Perfect matchings in balanced hypergraphs. Combinatorica. 16:1996;325-329.
15. M. Conforti, A. M. H. Gerards, and, A. Kapoor, A Theorem of Truemper, to appear. Preliminary version by M. Conforti and A. Kapoor, in, Lecture Notes in Computer Science, Integer Programming and Combinatorial Optimization, 6th IPCO Conference, Houston, pp. 53-68, 1988.
16. Conforti M., Rao M. R. Structural properties and recognition of restricted and strongly unimodular matrices. Math. Programming. 38:1987;17-27.
17. Conforti M., Rao M. R. Structural properties and decomposition of linear balanced matrices. Math. Programming. 55:1992;129-169.
18. Conforti M., Rao M. R. Odd cycles and matrices with integrality properties. Math. Programming. 45:1989;279-295.
19. Conforti M., Rao M. R. Properties of balanced and perfect matrices. Math. Programming. 55:1992;35-49.
20. Conforti M., Rao M. R. Testing balancedness and perfection of linear and star decomposable matrices. Math. Programming. 61:1993;1-18.
21. Cornuéjols G., Cunningham W. H. Compositions for perfect graphs. Discrete Math. 55:1985;245-254.
22. Cunningham W. H., Edmonds J. A combinatorial decomposition theory. Canad. J. Math. 22:1980;734-765.
23. Fulkerson D. R., Hoffman A., Oppenheim R. On balanced matrices. Math. Programming Study. 1:1974;120-132.
24. Golumbic M. C., Goss C. F. Perfect elimination and chordal bipartite graphs. J. Graph Theory. 2:1978;155-163.
25. Golumbic M. C. Algorithmic graph theory and perfect graphs. 1980;Academic Press.
26. Hall P. On representatives of subsets. J. London Math. Soc. 1935;26-30.
27. Hoffman A., Kolen A., Sakarovitch M. Characterizations of totally balanced and greedy matrices. SIAM journal of Algebraic and Discrete Methods. 6:1985;721-730.
28. Schrijver A. Theory of Linear and Integer Programming. 1986;Wiley, New York.
29. Seymour P. Decomposition of regular matroids. J. Combin. Theory Ser. B. 28:1980;305-359.
30. Truemper K. Alfa-balanced graphs and matrices and GF(3)-representability of matroids. J. Combin. Theory Ser. B. 32:1982;112-139.
31. Yannakakis M. On a class of totally unimodular matrices. Mathematics of Operations Research. 10:1985;280-304.