Algorithmica

, 7:465

# Forests, frames, and games: Algorithms for matroid sums and applications

• Harold N. Gabow
• Herbert H. Westermann
Article

## Abstract

This paper presents improved algorithms for matroid-partitioning problems, such as finding a maximum cardinality set of edges of a graph that can be partitioned intok forests, and finding as many disjoint spanning trees as possible. The notion of a clump in a matroid sum is introduced, and efficient algorithms for clumps are presented. Applications of these algorithms are given to problems arising in the study of the structural rigidity of graphs, the Shannon switching game, and others.

### Key words

Matroid Matroid sum Matroid partitioning Covering Arboricity Packing Bar-and-joint framework Bar-and-body framework Rigidity Shannon switching game

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