Abstract
The existence and efficient finding of small dominating sets in dense random graphs is examined in this work. We show, for the model G n,p with p=1/2, that: 1. The probability of existence of dominating sets of size less than log n tends to zero as n tends to infinity. 2. Dominating sets of size [log n] exist almost surely. 3. We provide two algorithms which construct small dominating sets in G n, 1/2 run in O (n alog n) time (on the average and also with high probability). Our algorithms almost surely construct a dominating set of size at most (1+e) log n, for any fixed e > 0.
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