Fernau, H. and Manlove, D. F. (2006) Vertex and Edge Covers With Clustering Properties: Complexity and Algorithms. In: Algorithms and Complexity in Durham 2006: Proceedings of the Second ACiD Workshop, Durham, UK, 18-20 Sep 2006, pp. 69-84. ISBN 9781904987383
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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 ttotal 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 N P-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.
| Item Type: | Conference Proceedings |
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| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Manlove, Professor David |
| Authors: | Fernau, H., and Manlove, D. F. |
| College/School: | College of Science and Engineering > School of Computing Science |
| ISBN: | 9781904987383 |
| Copyright Holders: | Copyright © 2006 The Authors |
| First Published: | First published in Algorithms and Complexity in Durham 2006: Proceedings of the Second ACiD Workshop: 69-84 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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