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Matematicheskie Zametki, 2021, Volume 109, Issue 1, Pages 36–46
DOI: https://doi.org/10.4213/mzm12784 (Mi mzm12784) 		 
This article is cited in 2 scientific papers (total in 2 papers)

First-Order Complexity of Subgraph Isomorphism via Kneser Graphs

V. A. Voronova, E. A. Dergachevb, M. E. Zhukovskiic, A. M. Neopryatnayab

a Caucasus Mathematical Center, Adyghe State University, Maikop
b Adyghe State University, Maikop
c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
Full-text PDF (482 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm12784
Abstract: The problem of finding the least number of variables of a first-order formula expressing the statement that an input-graph contains a subgraph isomorphic to a given pattern-graph is studied. Input-graphs of sufficiently high connectivity are considered. This problem has previously been solved for all pattern-graphs on four vertices except the simple cycle and the diamond graph. In the paper, this number is found for the two remaining graphs.
Keywords: Kneser graph, input-graph, pattern-graph, Ehrenfeucht game.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-2540.2020.1
Russian Science Foundation 18-71-00069
The work of M. E. Zhukovskii was supported by the Russian Science Foundation under grant 18-71-00069. The work of V. A. Voronov was supported by the program “Leading Scientific Schools” under grant NSh-2540.2020.1. Statement 1 was proved by V. A. Voronov. Statement 2 and the second part of Theorem 2 were proved by M. E. Zhukovskii. The work on the Introduction, Sec. 2, and the survey of known facts about the Kneser graphs and on the first part of Theorem 1 were carried out by A. M. Neopryatnaya and E. A. Dergachev.
Received: 06.05.2020
Revised: 23.06.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 1, Pages 29–37
DOI: https://doi.org/10.1134/S0001434621010041
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: Russian
Citation: V. A. Voronov, E. A. Dergachev, M. E. Zhukovskii, A. M. Neopryatnaya, “First-Order Complexity of Subgraph Isomorphism via Kneser Graphs”, Mat. Zametki, 109:1 (2021), 36–46; Math. Notes, 109:1 (2021), 29–37
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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