Journal of Universal Computer Science
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.
computational geometry, hypergraph, rigidity theory, matroid, pebble game
© Journal of Universal Computer Science
Lee, Audrey; Streinu, Ileana; and Theran, Louis, "Graded Sparse Graphs and Matroids" (2007). Computer Science: Faculty Publications, Smith College, Northampton, MA.