Using H(n,△,dm)to denote the family of all n vertices graphs with maximum degree at most △ and maximum density at most dm.A graph G is universal for H(we write G is H-universal),if G contains a copy of every graph H e H.Using probability methods to prove that when the probability p is greater than a certain threshold,a graph G～(G)(n,p)is high probability H(n,△,dm)-universality.
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