1+ Introductim ## 2. &tnatrsids An Z-nt~rfpis is 8 @-I matrix having thk. I+ 7 .Fyaty tha? some permuta-tion of its distinct ~ofutnns is the matrix J: I,\* fair some intttgcr r 2 '1. JP is the r \* r matrix of all 1's and lr is thbz F X r identity. Given an [-maitrix with r rows. the follc:wing pr
Fundamental circuits and a characterization of binary matroids
β Scribed by Michel Las Vergnas
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 84 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
Let F 7 denote the Fano matroid and e be a fixed element of F 7 . Let P(F 7 , e) be the family of matroids obtained by taking the parallel connection of one or more copies of F 7 about e. Let M be a simple binary matroid such that every cocircuit of M has size at least d 3. We show that if M does no
Let F 7 denote the Fano matroid and M be a simple connected binary matroid such that every cocircuit of M has size at least d 3. We show that if M does not have an F 7 -minor, M{F\* 7 , and d Γ [5, 6, 7, 8], then M has a circuit of size at least min[r(M )+1, 2d ]. We conjecture that the latter resul
~bl if and only if for each pair of , subsets R and S of E, such that IR (JSI ~3, either (i) VTcr E-(RUS), (RUT) E ZF+(SUT)E~