Vol. 9, No. 3, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Volume 13, Issue 4
Volume 13, Issue 3
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
Subscriptions
 
ISSN 2996-220X (online)
ISSN 2996-2196 (print)
Author Index
To Appear
 
Other MSP Journals
First-order definitions of subgraph isomorphism through the adjacency and order relations

Oleg Grigoryan, Mikhail Makarov and Maksim Zhukovskii

Vol. 9 (2020), No. 3, 293–302
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.

Keywords
first-order logic, subgraph isomorphism, order, logical complexity, quantifier depth
Mathematical Subject Classification 2010
Primary: 03C13, 68Q19
Milestones
Received: 3 December 2019
Revised: 6 February 2020
Accepted: 21 February 2020
Published: 15 October 2020
Authors
Oleg Grigoryan
Higher School of Economics
Moscow
Russia
Mikhail Makarov
Moscow Institute of Physics and Technology
Dolgoprudny
Russia
Maksim Zhukovskii
Laboratory of Advanced Combinatorics and Network Applications
Moscow Institute of Physics and Technology
Dolgoprudny
Russia