2022
DOI: 10.1007/s00453-022-00999-9
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Maximum Matching in Almost Linear Time on Graphs of Bounded Clique-Width

Abstract: Recently, independent groups of researchers have presented algorithms to compute a maximum matching in Õ(f (k) • (n + m)) time, for some computable function f , within the graphs where some clique-width upper bound is at most k (e.g., tree-width, modular-width and P4-sparseness). However, to the best of our knowledge, the existence of such algorithm within the graphs of bounded clique-width has remained open until this paper. Indeed, we cannot even apply Courcelle's theorem to this problem directly, because a … Show more

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