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A strengthened form of Tutte's characterization of regular matroids
- Source :
- Journal of Combinatorial Theory, Series B. 20:216-221
- Publication Year :
- 1976
- Publisher :
- Elsevier BV, 1976.
-
Abstract
- We prove the following theorem: A binary matroid is regular (totally unimodular) if and only if it has no submatroid that is a series extension of a Fano matroid or its dual. This theorem may be viewed as strengthening Tutte's celebrated characterization of regular matroids in the spirit of Kuratowski's theorem on planar graphs.
- Subjects :
- Discrete mathematics
Computer Science::Computer Science and Game Theory
Mathematics::Combinatorics
Fano plane
Matroid
Tutte theorem
Theoretical Computer Science
Planar graph
Combinatorics
Oriented matroid
symbols.namesake
Graphic matroid
Unimodular matrix
Computational Theory and Mathematics
Computer Science::Discrete Mathematics
symbols
Discrete Mathematics and Combinatorics
Matroid partitioning
Computer Science::Data Structures and Algorithms
Mathematics
Subjects
Details
- ISSN :
- 00958956
- Volume :
- 20
- Database :
- OpenAIRE
- Journal :
- Journal of Combinatorial Theory, Series B
- Accession number :
- edsair.doi.dedup.....614eb864014921fca367081a99fae704
- Full Text :
- https://doi.org/10.1016/0095-8956(76)90012-5