Year: 2007
Type: preprint
Abstract: Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of generically rigid structures. We define a new family called {\bf graded sparse graphs}, arising from generically pinned (completely immobilized) bar-and-joint frameworks and prove that they also form matroids. We address five problems on graded sparse graphs: {\bf Decision}, {\bf Extraction}, {\bf Components}, {\bf Optimization}, and {\bf Extension}. We extend our {\bf pebble game algorithms} to solve them.
Source: arXiv (Cornell University)
Authors: Lee, Audrey, Streinu, Ileana, Theran, Louis
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1590975346