Minimum Connected Dominating Sets of Random Cubic Graphs

@article{Duckworth2002MinimumCD,
  title={Minimum Connected Dominating Sets of Random Cubic Graphs},
  author={William Duckworth},
  journal={Electr. J. Comb.},
  year={2002},
  volume={9}
}
We present a simple heuristic for finding a small connected dominating set of cubic graphs. The average-case performance of this heuristic, which is a randomised greedy algorithm, is analysed on random n-vertex cubic graphs using differential equations. In this way, we prove that the expected size of the connected dominating set returned by the algorithm is asymptotically almost surely less than 0.5854n. 

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