Minimum Power Dominating Sets of Random Cubic Graphs
Liying Kang, Nicholas Wormald · Journal of Graph Theory · 2016
Abstract We present two heuristics for finding a small power dominating set of cubic graphs. We analyze the performance of these heuristics on random cubic graphs using differential equations. In this way, we prove that the proportion of vertices in a minimum power dominating set of a random cubic graph is asymptotically almost surely at most 0.067801. We also provide a corresponding lower bound of using known results on bisection width.