Total Domination, Connected Vertex Cover and Steiner Tree with Conflicts

Abstract

Total dominating set, connected vertex cover and Steiner tree are well-known graph problems. Despite the fact that they are NP-complete to optimize, it is easy (even trivial) to find solutions, regardless of their size. In this paper, we study a variant of these problems by adding conflicts, that are pairs of vertices that cannot be both in a solution. This new constraint leads to situations where it is NP-complete to decide if there exists a solution avoiding conflicts. This paper proposes NP-completeness proofs of the existence of a solution for different restricted classes of graphs and conflicts, improving recent results. We also propose polynomial time constructions in several restricted cases and we introduce a new parameter, the stretch, to capture the locality of the conflicts.

Keywords

• np- completeness
• steiner tree
• total dominating set
• graph theory
• conflicts
• connected vertex cover
• forbidden pairs
• graphs
• conflicts
• [info.info-ro] computer science [cs]/operations research [cs.ro]