%0 Journal Article
%T A Constructive Characterisation of Circuits in the Simple (2,2)-sparsity Matroid
%A Anthony Nixon
%J Computer Science
%D 2012
%I arXiv
%X 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 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.
%U http://arxiv.org/abs/1202.3294v2