The independent domination number of a random graph

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2011 English Publisher:University of Zielona Góra, PolandJournal:Discussiones Mathematicae Graph Theory, volume 31, page 129 (issn: 1234-3099, eissn: 2083-5892,

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Authors: Lane H. Clark; Darin Johnson;

doi: 10.7151/dmgt.1533

The independent domination number of a random graph

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Abstract

We prove a two-point concentration for the independent domination number of the random graph Gn,p provided p 2 ln(n) � 64ln((lnn)=p). occurs asymptotically almost surely (a.a.s.) if P(Gn;p has property A) ! 1 as n ! 1 . See Bollobas (2) for notation and terminology. Weber (7) showed if p = 1=2 then a.a.s. (Gn;p) is either blog2 n − log2(log2 nlnn)c + 1 or blog2 n − log2(log2 nlnn)c + 2 and a.a.s. i(Gn;p)

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