We give a strongly polynomial-time algorithm minimizing a submodular function f given by a value-giving oracle. The algorithm does not use the ellipsoid method or any other linear programming method. No bound on the complexity of the values of f is needed to be known a priori. The number of oracle c
Submodular functions in graph theory
✍ Scribed by András Frank
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 819 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
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 adding a minimum number of edges.
📜 SIMILAR VOLUMES
## Abstract The aim of this note is to give an account of some recent results and state a number of conjectures concerning extremal properties of graphs.
## Abstract A list of 31 problems presented here reflects some of the main trends in topological graph theory.
Given two graphs G=(X,E), H=(Y,F); If AcX and if f is a function from A to Y, we pose the problem of deciding if f can be extended into a homomorphism from G to H. We know how to solve this problem when H is, for instance, a tree, or a chordal graph. We give here a solution to this problem when g is