Minimum independent dominating sets of random cubic graphs

Authors:
W. Duckworth;N. C. Wormald
Affiliations:
Department of Computing, Macquarie University, Australia;Department of Mathematics & Statistics, University of Melbourne, Australia
Venue:
Random Structures & Algorithms
Year:
2002

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Abstract

We present a heuristic for finding a small independent dominating set D of cubic graphs. We analyze the performance of this heuristic, which is a random greedy algorithm, on random cubic graphs using differential equations, and obtain an upper bound on the expected size of D. A corresponding lower bound is derived by means of a direct expectation argument. We prove that D asymptotically almost surely satisfies 0.2641n ≤ |D| ≤ 0.27942n.