Random graphs and Lindstrom quantifiers for natural graph properties

Simi Haber; Saharon Shelah

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arXiv · 1510.06574

Random graphs and Lindstrom quantifiers for natural graph properties

Simi Haber·Saharon Shelah

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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.

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BibTeX RIS

Simi Haber, Saharon Shelah. 2015-10-22. Random graphs and Lindstrom quantifiers for natural graph properties. https://arxiv.org/abs/1510.06574

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