Simultaneous Dominating Set for Spanning Tree Factorings
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For a connected graph G we call a set F a spanning tree factoring of G if it contains all spanning trees of G. A subset S⊆ V(G) is a simultaneous dominating set of G if it is a dominating set in every spanning tree in F. We consider the problem of finding a minimum size simultaneous dominating set for spanning tree factorings. We show that the decision version of this problem is NP-complete by pointing out its close relation to the vertex cover problem. We present an exact algorithm to solve this problem and show how to solve it in polynomial time on some graph classes like bipartite or chordal graphs. Moreover, we derive a 2-approximation algorithm for this problem.
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