We strengthen a result by Laskar and Lyle (Discrete Appl. Math. 157, 330–338 2009) by proving that it is NP-complete to decide whether a bipartite planar graph can be partitioned into three independent dominating sets. In contrast, we show that this is always possible for every maximal outerplanar graph with at least three vertices. Moreover, we extend their previous result by proving that deciding whether a bipartite graph can be partitioned into k independent dominating sets is NP-complete for every k ≥ 3. We also strengthen a result by Henning et al. (Discrete Math. 309(23), 6451–6458 2009) by showing that it is NP-complete to determine if a graph has two disjoint independent dominating sets, even when the problem is restricted to triangle-free planar graphs. Finally, for every k ≥ 3, we show that there is some constant t depending only on k such that deciding whether a k-regular graph can be partitioned into t independent dominating sets is NP-complete. We conclude by deriving moderately exponential-time algorithms for the problem.

我们通过加强和拉斯卡尔莱尔（离散应用数学。结果157通过证明它是一个NP完全决定一个双向平面图形是否可以划分为三个独立支配集，330-338 2009）。相反，我们表明，对于每个至少具有三个顶点的最大外平面图，这始终是可能的。此外，我们通过证明决定一个二分图是否可以被划分为延长其前面的结果ķ独立支配集是NP完全为每ķ ≥3.我们也亨宁等加强的结果。（离散数学309（23），6451–6458 2009）通过证明确定一个图是否具有两个不相交的独立控制集是NP完全的，即使该问题仅限于无三角形平面图也是如此。最后，对于每一个≥3的k，我们表明存在一个仅取决于k的常数t，因此确定k正则图是否可以划分为t个独立的主导集是NP完全的。我们通过导出适度指数时间算法来解决问题。