New algorithms recognize (k,ℓ)-sparse graphs in near-linear time for 0 ≤ ℓ ≤ k and subquadratic time for k < ℓ < 2k using orientations, arc-connectivity, and centroid decomposition.
Frank.Connections in combinatorial optimization, volume 38
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Asymptotically faster algorithms for recognizing $(k,\ell)$-sparse graphs
New algorithms recognize (k,ℓ)-sparse graphs in near-linear time for 0 ≤ ℓ ≤ k and subquadratic time for k < ℓ < 2k using orientations, arc-connectivity, and centroid decomposition.