2012/02/15 by Anthony Nixon, Nixon, Anthony
Computer Science · Engineering · Materials Science · Mathematics · #05B35 #52C25 #Advanced Materials and Mechanics #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Structural Analysis and Optimization #Supramolecular Self-Assembly in Materials #cs.DM #math.CO #msc:05B35 #msc:52C25
paper · pdf · doi:10.48550/arxiv.1202.3294
22 pages, 6 figures. Changes to presentation
openalex publication_date 2012/02/15 · arxiv created 2013/06/21 · arxiv updated 2013/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.