Graded Sparse Graphs and Matroids

: Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures. We define a new family called graded sparse graphs, arising from generically pinned bar-and-joint frameworks, and prove that they also form matroids. We also address several algorithmic problems on graded sparse graphs: Decision, Spanning, Extraction, Components, Optimization, and Extension. We sketch variations on pebble game algorithms to solve them. Key Words: computational geometry, hypergraph, rigidity theory, matroid, pebble game Category: F.2.2, G.2.2

• Type: Journal
• Year: 2007
• Where: JUCS
• Authors: Audrey Lee, Ileana Streinu, Louis Theran
• Keywords: JUCS 2007, Matroid, Rigidity Theory, Sparse Graphs