A constructive characterisation of circuits in the simple (2,2)-sparsity matroid

Nixon, Anthony (2014) A constructive characterisation of circuits in the simple (2,2)-sparsity matroid. European Journal of Combinatorics, 42. pp. 92-106. ISSN 0195-6698

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Abstract

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 where the number of edges induced by any X⊊V is at most 2|X|−2. Insisting on simplicity results in the Henneberg 2 operation being adequate only when the graph is sufficiently connected. Thus we introduce 3 different join 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.

Item Type:
Journal Article
Journal or Publication Title:
European Journal of Combinatorics
Additional Information:
The final, definitive version of this article has been published in the Journal, European Journal of Combinatorics 42, 2014, © ELSEVIER.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2614
Subjects:
ID Code:
71103
Deposited By:
Deposited On:
06 Oct 2014 11:11
Refereed?:
Yes
Published?:
Published
Last Modified:
27 Sep 2020 02:16