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    Rights statement: The final, definitive version of this article has been published in the Journal, European Journal of Combinatorics 42, 2014, © ELSEVIER.

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

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>11/2014
<mark>Journal</mark>European Journal of Combinatorics
Volume42
Number of pages15
Pages (from-to)92-106
Publication StatusPublished
Early online date20/06/14
<mark>Original language</mark>English

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.

Bibliographic note

The final, definitive version of this article has been published in the Journal, European Journal of Combinatorics 42, 2014, © ELSEVIER.