Independent Domination in Triangle Graphs

We study the complexity of INDEPENDENT DOMINATION, a well-known algorithmical problem, for triangle graphs, i.e., graphs G satisfying the following triangle condition: for every maximal independent set I in G and every edge uv in G−I, there is a vertex w∈I such that {u,v,w} induces a triangle in G. We show that INDEPENDENT DOMINATION within triangle graphs is closely connected with the general STABLE MAX-CUT problem. However, the INDEPENDENT DOMINATION problem is NP-complete for K1,4-free triangle graphs. Finally, we investigate some natural invariants related to independent domination from the algorithmical point of view and apply our results to triangle graphs.