Minimum Connected Dominating Sets of Random Cubic Graphs

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.

• Type: Journal
• Year: 2002
• Where: COMBINATORICS
• Authors: William Duckworth
• Keywords: COMBINATORICS 2002, Cubic Graphs, N-vertex Cubic Graphs, Randomised Greedy Algorithm