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ACID

2006

2006

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.

Related Content

Added |
30 Oct 2010 |

Updated |
30 Oct 2010 |

Type |
Conference |

Year |
2006 |

Where |
ACID |

Authors |
Henning Fernau, David Manlove |

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