## Paper: Zero-one laws for Gilbert random graphs (at LICS 1996)

**Gregory L. McColm**

### Abstract

We look at a competitor of the Erdos-Renyi models of random graphs, one proposed by E. Gilbert (1961): given /spl delta/>0 and a metric space X of diameter >/spl delta/, scatter n vertices at random on X and connect those of distance apart: we get a random graph G/sub n,/spl delta///sup X/. Question: for fixed X, /spl delta/, do we have 0-1 laws for FO logic? We prove that this is true if X is a circle.

### BibTeX

@InProceedings{McColm-ZeroonelawsforGilbe, author = {Gregory L. McColm}, title = {Zero-one laws for Gilbert random graphs}, booktitle = {Proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science (LICS 1996)}, year = {1996}, month = {July}, pages = {360--369}, location = {New Brunswick, NJ, USA}, publisher = {IEEE Computer Society Press} }