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First-order
definitions of subgraph isomorphism through the adjacency and
order relations
Oleg Grigoryan, Mikhail Makarov and Maksim Zhukovskii |
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Vol. 9 (2020), No. 3, 293–302
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Abstract |
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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 vertices. |
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Keywords
first-order logic, subgraph isomorphism, order, logical
complexity, quantifier depth
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Mathematical Subject Classification 2010
Primary: 03C13, 68Q19
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Milestones
Received: 3 December 2019
Revised: 6 February 2020
Accepted: 21 February 2020
Published: 15 October 2020
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Authors |
| Oleg Grigoryan | |
| Higher School of Economics Moscow Russia |
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| Mikhail Makarov | |
| Moscow Institute of Physics and
Technology Dolgoprudny Russia |
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| Maksim Zhukovskii | |
| Laboratory of Advanced Combinatorics
and Network Applications Moscow Institute of Physics and Technology Dolgoprudny Russia |
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