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.
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Submitted on : Tuesday, December 19, 2017 - 7:57:56 AM
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Alexis Cornet, Christian Laforest. Total Domination, Connected Vertex Cover and Steiner Tree with Conflicts. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2017, Vol 19 no. 3 (3). ⟨hal-01455072v3⟩



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