On the Domination Number of a Random Graph

نویسندگان

  • Ben Wieland
  • Anant P. Godbole
چکیده

In this paper, we show that the domination number D of a random graph enjoys as sharp a concentration as does its chromatic number χ. We first prove this fact for the sequence of graphs {G(n, pn}, n → ∞, where a two point concentration is obtained with high probability for pn = p (fixed) or for a sequence pn that approaches zero sufficiently slowly. We then consider the infinite graph G(Z+, p), where p is fixed, and prove a three point concentration for the domination number with probability one. The main results are proved using the second moment method together with the Borel Cantelli lemma.

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عنوان ژورنال:
  • Electr. J. Comb.

دوره 8  شماره 

صفحات  -

تاریخ انتشار 2001