Minimum independent dominating sets of random cubic graphs

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. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 147–161, 2002