Pebble game algorithms and sparse graphs

@article{John2008PebbleGA,
  title={Pebble game algorithms and sparse graphs},
  author={A. L. John and I. Streinu},
  journal={ArXiv},
  year={2008},
  volume={abs/math/0702129}
}
  • A. L. John, I. Streinu
  • Published 2008
  • Mathematics, Computer Science
  • ArXiv
  • A multi-graph $G$ on n vertices is $(k,l)$-sparse if every subset of $n'≤n$ vertices spans at most $kn'-l$ edges, $0 ≤l < 2k$. $G$ is tight if, in addition, it has exactly $kn - l$ edges. We characterize $(k,l)$-sparse graphs via a family of simple, elegant and efficient algorithms called the $(k,l)$-pebble games. As applications, we use the pebble games for computing components (maximal tight subgraphs) in sparse graphs, to obtain inductive (Henneberg) constructions, and, when $l=k$, edge… CONTINUE READING
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