@techReport{Fernau:2008:8137,
	      Author = {Fernau,H.;Manlove,D.F.},
	       Institution = {University of Glasgow, Department of Computing Science},
                          Title = {Vertex and Edge Covers with Clustering Properties: Complexity and Algorithms}, 
                          ISBN =
	      {TR-2006-210},
	      abstract = {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 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},Publisher =
	      {Dept of Computing Science, University of Glasgow},
	      Year = {2006}}