Connectivity of submodular functions
β Scribed by James Oxley; Geoff Whittle
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 788 KB
- Volume
- 105
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
The notion of connectivity for submodular functions was introduced by Cunningham. This paper relates the connectivity of such a function f to that of certain submodular functions which are derived from j In particular, we prove a generalisation of the well-known matroid result that, for every element x of a connected matroid from M is connected.
M, either the deletion or contraction of x
π SIMILAR VOLUMES
After providing a simple characterization of Horn functions (i.e., those Boolean functions that have a Horn DNF), we study in detail the special class of submodular functions. Every prime implicant of such a function involves at most one complemented and at most one uncomplemented variable, and base
Frank, A., Submodular functions in graph theory, Discrete Mathematics 111 (1993) 231-243. We describe various aspects of the use of submodular functions in graph theory. New proofs of theorems of Mader and of Tutte are provided as well as a new application on making a digraph k-edge-connected by ad