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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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