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A characterization of box-Mengerian matroid ports
Chen, Xujin1; Ding, Guoli2; Zang, Wenan3
AbstractLet M be a matroid on E boolean OR {1}, where 1 is not an element of E is a distinguished element of M. The l-port of M is the set P = {P: P subset of E with P boolean OR {1} a circuit of M}. Let A be the P-E incidence matrix. Let U(2,4) be the uniform matroid on four elements of rank two, let F(7) be the Fano matroid, let F*(7) be the dual of F(7), and let F(7)(+) be the unique series extension of F(7). In this paper, we prove that the system Ax >= 1, x >= 0 is box-totally dual integral (box-TDI) if and only if M has no U(2,4)-minor using 1, no F*(7)-minor using 1, and no F(7)(+)-minor using 1 as a series element. Our characterization yields a number of interesting results in combinatorial optimization.
Keywordbinary clutter binary matroid regular matroid box-total dual integrality
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000256197100015
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Document Type期刊论文
Corresponding AuthorChen, Xujin
Affiliation1.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China
2.Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
3.Univ Hong Kong, Dept Math, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Chen, Xujin,Ding, Guoli,Zang, Wenan. A characterization of box-Mengerian matroid ports[J]. MATHEMATICS OF OPERATIONS RESEARCH,2008,33(2):497-512.
APA Chen, Xujin,Ding, Guoli,&Zang, Wenan.(2008).A characterization of box-Mengerian matroid ports.MATHEMATICS OF OPERATIONS RESEARCH,33(2),497-512.
MLA Chen, Xujin,et al."A characterization of box-Mengerian matroid ports".MATHEMATICS OF OPERATIONS RESEARCH 33.2(2008):497-512.
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