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Asymptotically Faster Algorithms for Recognizing $(k,\ell)$-Sparse Graphs
For fixed integers $k,\ell$ with $0\leq\ell<3k$, we study the problem of deciding whether a graph is $(k,\ell)$-sparse, a notion arising in combinatorial optimization and rigidity theory. Standard pebble-game algorithms take $O(n^2)$ time for $0\leq\ell<2k$ and $O(n^3)$ time for $2k\leq\ell<3k$, alt
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