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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/Magazine › Journal article › peer-review

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A constructive characterisation of circuits in the simple (2,2)-sparsity matroid. / Nixon, Anthony.
In: European Journal of Combinatorics, Vol. 42, 11.2014, p. 92-106.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Nixon, A 2014, 'A constructive characterisation of circuits in the simple (2,2)-sparsity matroid', European Journal of Combinatorics, vol. 42, pp. 92-106. https://doi.org/10.1016/j.ejc.2014.05.009

APA

Nixon, A. (2014). A constructive characterisation of circuits in the simple (2,2)-sparsity matroid. European Journal of Combinatorics, 42, 92-106. https://doi.org/10.1016/j.ejc.2014.05.009

Vancouver

Nixon A. A constructive characterisation of circuits in the simple (2,2)-sparsity matroid. European Journal of Combinatorics. 2014 Nov;42:92-106. Epub 2014 Jun 20. doi: 10.1016/j.ejc.2014.05.009

Author

Nixon, Anthony. / A constructive characterisation of circuits in the simple (2,2)-sparsity matroid. In: European Journal of Combinatorics. 2014 ; Vol. 42. pp. 92-106.

Bibtex

@article{e0a17e1f27e34cfb86a70ab9a6f90c97,
title = "A constructive characterisation of circuits in the simple (2,2)-sparsity matroid",
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.",
author = "Anthony Nixon",
note = "The final, definitive version of this article has been published in the Journal, European Journal of Combinatorics 42, 2014, {\textcopyright} ELSEVIER.",
year = "2014",
month = nov,
doi = "10.1016/j.ejc.2014.05.009",
language = "English",
volume = "42",
pages = "92--106",
journal = "European Journal of Combinatorics",
issn = "0195-6698",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - A constructive characterisation of circuits in the simple (2,2)-sparsity matroid

AU - Nixon, Anthony

N1 - The final, definitive version of this article has been published in the Journal, European Journal of Combinatorics 42, 2014, © ELSEVIER.

PY - 2014/11

Y1 - 2014/11

N2 - 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.

AB - 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.

U2 - 10.1016/j.ejc.2014.05.009

DO - 10.1016/j.ejc.2014.05.009

M3 - Journal article

VL - 42

SP - 92

EP - 106

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

ER -