DOIAbstract
AbstractThe paper sets out to investigate the degree sequences d1⩾d2⩾…⩾dn of random graphs of order n in which the edges are chosen independently and with the same probability p, 0<p<1. The main aim is to find small intervals which contain the mth degree, dm, of almost every (a.e.) graph. It is shown that if m varies arbitrarily in the interval 1⩽m⩽12n and C(n)→∞ arbitrarily slowly, then there is an interval of length C(n) (n⧸log (n⧸m))12 which contains the mth highest degree, dm, of a.e. graph. If m grows slowly with n (in particular if m = 1, that is dm = d1 is the maximal degree), the centre of this interval is given by a simple expression.Other results concern the jumps dm −dm+1 in the degree sequence of a.e. graph, the repeated values ...
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