A base of the cycle space of a binary matroid M on E is said to be convex if its elements can be totally ordered in such a way that for every e E E tk set of elements of the base containing e is an interval. \'Ure show that a binary matroid is cographic iff it has a convex base of cycles; equivalent
On matroids and hierarchial graphs
✍ Scribed by David Fernández-Baca; Mark A. Williams
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 601 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0020-0190
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Mader proved that every 2-connected simple graph G with minimum degree d exceeding three has a cycle C, the deletion of whose edges leaves a 2-connected graph. Jackson extended this by showing that C may be chosen to avoid any nominated edge of G and to have length at least d-1. This article proves
Let K be a connected and undirected graph, and M be the polygon matroid of K . Assume that, for some k 2 1, the matroid M is kseparable and k-connected according to the matroid separability and connectivity definitions of W. T. Tutte. In this paper we classify the matroid kseparations of M in terms
A frame matroid is any submatroid of a matroid in which cach point belongs to a line spanned by a fixed basis. A biased graph is a graph with certain polygons called balanced, no theta graph containing exactly two balanced polygons. We prove that certain matroids, called bias matroids, of biased gra
A graph is antipodal if, for every vertex c', there exists exactly one vertex V which is not closer to r than every vertex adjacent to 6. In this paper we consider the problem of characterizing tope graphs of oriented matroids, which constitute a broad class of antipodal graphs. One of the results i
An element e of a 3-connected matroid M is essential if neither the deletion M\e nor the contraction M/e is 3-connected. Tutte's Wheels and Whirls Theorem proves that the only 3-connected matroids in which every element is essential are the wheels and whirls. In this paper, we consider those 3-conne