Rota's conjecture about n bases in a rank n matroid is solved for n = 3.
Base exchange properties of graphic matroids
β Scribed by Marcel Wild
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 663 KB
- Volume
- 148
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
In this paper we present the characterization of graphic matroids using the concept of a chord. Then we apply this characterization to solve a problem of Szamkolowicz [9]. One of the deepest theorems in the theory of matroids is Tuttes excludedminor characterization of graphic matroids [ 111. The p
## Abstract In this paper we present a relatively simple proof of Tutt's characterization of graphic matroids. The proof uses the notion of βsigned graphβ and it is βgraphicβ in the sense that it can be presented almost entirely by drawing (signed) graphs. Β© 1995 John Wiley & Sons, Inc.
We give a counterexample to a conjecture by Wild about binary matroids. We connect two equivalent lines of research in matroid theory: a simple type of basis-exchange property and restrictions on the cardinalities of intersections of circuits and cocircuits. Finally, we characterize direct sums of s