Extension of zero-one k-law

2013/04/03 by M. E. Zhukovskii, Zhukovskii, M. E.
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR

paper · pdf · doi:10.48550/arxiv.1304.0900

in Russian

arxiv created 2013/04/03 · arxiv updated 2013/04/04

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.

Related

• Universal Zero-One k--Law
• Random Graph: Stronger logic but with the zero one law
• Zero-one laws for k-variable first-order logic of sparse random graphs
• Hereditary Zero-One Laws for Graphs
• Failure of 0-1 law for sparse random graph in strong logics