Random graphs and Lindstrom quantifiers for natural graph properties
Logic
2015-10-23 v1
Abstract
We study zero-one laws for random graphs. We focus on the following question that was asked by many: Given a graph property P, is there a language of graphs able to express P while obeying the zero-one law? Our results show that on the one hand there is a (regular) language able to express connectivity and k-colorability for any constant k and still obey the zero-one law. On the other hand we show that in any (semiregular) language strong enough to express Hamiltonicity one can interpret arithmetic and thus the zero-one law fails miserably. This answers a question of Blass and Harary.
Keywords
Cite
@article{arxiv.1510.06574,
title = {Random graphs and Lindstrom quantifiers for natural graph properties},
author = {Simi Haber and Saharon Shelah},
journal= {arXiv preprint arXiv:1510.06574},
year = {2015}
}