Graded sparse graphs and body-length-direction frameworks. (May 2015)

• Record Type: Journal Article
• Authors: Jackson, Bill; Nguyen, Viet Hang
• Is Part Of: European journal of combinatorics. Volume 46(2015:May)
• Page Start: 51
• Page End: 67
• Publication Date: 2015-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2014.10.010
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We consider graded sparse graphs: graphs satisfying different sparsity conditions for different types of edges. We provide an inductive construction for these graphs and a decomposition into 'graded pseudoforests' i.e. spanning subgraphs in which each connected component contains at most one cycle and in which the edges in such a cycle are restricted by the grading. The decomposition is used to obtain combinatorial characterisations of rigidity in different types of body-length-direction frameworks. We also study graded sparse graphs from a matroid view point and derive the rank function as well as a decomposition for matroids defined by graded sparse graphs.