Extension of zero-one k-law

Abstract

We study an asymptotic behavior of the probabilities of first-order properties of random graph G(N,p) in the article. We conider p such that lnp=-alnN, a>0. We find values of parameter a from (1-exp(ln2(1-k)),1) such that the random graph obeys zero-one k-law.

arXiv commentin Russian

References in corpus (1)

• On the convergence of probabilities of the random graphs' properties expressed by first-order formulae with a bounded quantifier depth