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2020 First-order definitions of subgraph isomorphism through the adjacency and order relations
Oleg Grigoryan, Mikhail Makarov, Maksim Zhukovskii
Mosc. J. Comb. Number Theory 9(3): 293-302 (2020). DOI: 10.2140/moscow.2020.9.293

Abstract

We study first-order definitions of graph properties over the vocabulary consisting of the adjacency and order relations. We compare logical complexities of subgraph isomorphism in terms of the minimum quantifier depth in two settings: with and without the order relation. We prove that, for pattern-trees, it is at least (roughly) two times smaller in the former case. We find the minimum quantifier depths of <-sentences defining subgraph isomorphism for all pattern graphs with at most 4 vertices.

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Oleg Grigoryan. Mikhail Makarov. Maksim Zhukovskii. "First-order definitions of subgraph isomorphism through the adjacency and order relations." Mosc. J. Comb. Number Theory 9 (3) 293 - 302, 2020. https://doi.org/10.2140/moscow.2020.9.293

Information

Received: 3 December 2019; Revised: 6 February 2020; Accepted: 21 February 2020; Published: 2020
First available in Project Euclid: 22 October 2020

zbMATH: 07272350
MathSciNet: MR4164870
Digital Object Identifier: 10.2140/moscow.2020.9.293

Subjects:
Primary: 03C13, 68Q19

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.9 • No. 3 • 2020
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