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Pebble Game Algorithms and (k,l)-Sparse Graphs

Abstract : 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-disjoint tree decompositions.
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https://hal.inria.fr/hal-01184350
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Audrey Lee, Ileana Streinu. Pebble Game Algorithms and (k,l)-Sparse Graphs. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.181-186. ⟨hal-01184350⟩

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