A cycle in a matroid is a disjoint union of circuits. This paper proves that every regular matroid M without coloops has a set S of cycles whose union is E(M) such that every element is in at most three of the cycles in S. It follows immediately from this that, on average, each element of M is in at
Cycle covering of binary matroids
β Scribed by Ury Jamshy; Michael Tarsi
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 408 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
It is shown that each binary matroid contains an odd number of maximal cycles and, as a result of this, that each element of an Eulerian binary matroid is contained in an odd number of circuits. Let M be a binary matroid with circuits ~(M) and cycles .~(M), and let ~e(M) be the set of circuits conta
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