𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The cocycle lattice of binary matroids, II

✍ Scribed by László Lovász; Ákos Seress

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
836 KB
Volume
226-228
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

The Cocycle Lattice of Binary Matroids
The Cocycle Lattice of Binary Matroids
✍ László Lovász; Ákos Seress 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 330 KB

We study the lattice (grid) generated by the incidence vectors of cocycles of a binary matroid and its dual tattice. We characterize those binary matroids for which the obvious necessary conditions for a vector to belong to the cocycle lattice are also sufficient. This characterization yields a poly

Large Circuits in Binary Matroids of Lar
Large Circuits in Binary Matroids of Large Cogirth, II
✍ Winfried Hochstättler; Bill Jackson 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 223 KB

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  [5, 6, 7, 8], then M has a circuit of size at least min[r(M )+1, 2d ]. We conjecture that the latter resul

On the Connectivity Function of a Binary
On the Connectivity Function of a Binary Matroid
✍ Manoel Lemos 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 210 KB

In this paper, we shall consider the following problem: up to duality, is a connected matroid reconstructible from its connectivity function? Cunningham conjectured that this question has an affirmative answer, but Seymour gave a counter-example for it. In the same paper, Seymour proved that a conne

Weight distribution of the bases of a bi
Weight distribution of the bases of a binary matroid
✍ S. Zhou 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 399 KB

Let M be a weighted binary matroid and UJ~ < . < w,,, be the increasing sequence of all possible distinct weights of bases of M. We give a sufficient condition for the property that Wl,..., wm is an arithmetical progression of common difference d. We also give conditions which guarantee that wi+l -w