Computing at Glasgow University
Paper ID: 8967

Vertex and edge covers with clustering properties: complexity and algorithms
Fernau,H. Manlove,D.F.

Publication Type: Journal
Appeared in: Journal of Discrete Algorithms, volume 7, number 2
Page Numbers : 149-167
Publisher: Elsevier Science
Year: 2009

URL: This publication is available at this URL.


We consider the concepts of a t-total vertex cover and a t- total edge cover (t >= 1), which generalise 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 at least t vertices (edges). These definitions are motivated by combining the concepts of clustering and covering in graphs. Moreover they yield a spectrum of parameters that essentially range from a vertex cover to a connected vertex cover (in the vertex case) and from an edge cover to a spanning tree (in the edge case). For various values of t, we present NP-completeness and approximability results (both upper and lower bounds) and FPT algorithms for problems concerned with finding the minimum size of a t-total vertex cover, t-total edge cover and connected vertex cover, in particular improving on a previous FPT algorithm for the latter problem.

Keywords: Algorithm; NP-completeness; approximability; t-total vertex cover; connected vertex cover; t-total edge cover

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