A Constructive Characterisation of Circuits in the Simple (2,2)-sparsity Matroid

Details A Constructive Characterisation of Circuits in the Simple (2,2)-sparsity Matroid A Constructive Characterisation of Circuits in the Simple (2,2)-sparsity Matroid

2012-02-15

arxiv.org/abs/1202.3294v1

Mathematics

Combinatorics

27 pages, 13 figures

Scientific paper

We provide a constructive characterisation of circuits in the simple (2,2)-sparsity matroid. A circuit is a simple graph G=(V,E) with |E|=2|V|-1 and the number of edges induced by any $X \subsetneq V$ is at most 2|X|-2. Insisting on simplicity results in the Henneberg operation being enough only when the graph is sufficiently connected. Thus we introduce 3 different sum operations to complete the characterisation. Extensions are discussed to when the sparsity matroid is connected and this is applied to the theory of frameworks on surfaces to provide a conjectured characterisation of when frameworks on an infinite circular cylinder are generically globally rigid.

Affiliated with

Also associated with

No associations

Rating

A Constructive Characterisation of Circuits in the Simple (2,2)-sparsity Matroid does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Constructive Characterisation of Circuits in the Simple (2,2)-sparsity Matroid, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Constructive Characterisation of Circuits in the Simple (2,2)-sparsity Matroid will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-557643