The Curse of Connectivity: t-Total Vertex (Edge) Cover
نویسندگان
چکیده
We investigate the effect of certain natural connectivity constraints on the parameterized complexity of two fundamental graph covering problems, namely k-VERTEX COVER and k-EDGE COVER. Specifically, we impose the additional requirement that each connected component of a solution have at least t vertices (resp. edges from the solution), and call the problem t-TOTAL VERTEX COVER (resp. t-TOTAL EDGE COVER). We show that – both problems remain fixed-parameter tractable with these restrictions, with running times of the form O∗ `
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Vertex and Edge Covers with Clustering Properties: Complexity and Algorithms
We consider the concepts of a t-total vertex cover and a t-total edge cover (t ≥ 1), which generalize the notions of a vertex cover and an edge cover, respectively. A t-total vertex (respectively edge) cover of a connected graph G is a vertex (edge) cover S of G such that each connected component of the subgraph of G induced by S has least t vertices (edges). These definitions are motivated by ...
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