In 1959 Tutte gave a minor characterization of graphic matroids. Within the framework of greedoids, a natural analogue of the cycle matroid in graphs is the branching greedoid. Schmidt has shown that, similar to Tutte's result, branching greedoids can be characterized by forbidden minors. Here we g
A Characterization of Mixed Branching Greedoids
β Scribed by Steven J. Tedford
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 211 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0218-0006
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## Abstract A result of Korte and LovΓ‘sz states that the basis graph of every 2β connected greedoid is connected. We prove that the basis graph of every 3βconnected branching greedoid is (Ξ΄ ββ 1)βconnected, where Ξ΄ is the minimum inβdegree (disregarding the root) of the underlying rooted directed (
Let \(p_{n}\) denote the maximum number of paths a greedoid over \(n\) elements can have. As an upper bound, we of course have \(p_{n}<2^{n}\). We establish a lower bound for the maximum: \(1.6 \cdot 3^{n / 3}<p_{n}\). In the class of simple greedoids (those greedoids on \(n\) elements having exactl
An algebraic charactcrlzatlon of branching of skeletal forms is proposed which IS based on the concept of the comparability of functions as defined by Muirhead. The approach allows a rigorous definition of the concept of branch@ and susgests that structures having an identical distribution of valenc