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Let Pℓ denote a path in a graph G=(V,E) with ℓ vertices. A vertex cover Pℓ set C in G is a vertex subset such that every Pℓ in G has at least a vertex in C. The Vertex CoverPℓ problem is to find a vertex cover Pℓ set of minimum cardinality in a given graph. This problem is NP-hard for any integer ℓ⩾2. The parameterized version of Vertex CoverPℓ problem called k-Vertex CoverPℓ asks whether there exists...
An induced matching $$M\subseteq E$$ M ⊆ E in a graph $$G=(V, E)$$ G = ( V , E ) is a matching such that no two edges in $$M$$ M are joined by any third edge of the graph. The Maximum Induced Matching problem is to find an induced matching of maximum cardinality. It is NP-hard. Branch-and-reduce algorithms proposed in the previous results for the Maximum Induced Matching...
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