Enviar artigo por via de e-mail Logical complexity of induced subgraph isomorphism for certain families of graphs
- Autores: Zhukovskii M.E.1,2, Kudryavtsev E.D.3, Makarov M.V.3, Shlychkova A.S.3
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Afiliações:
- Advanced Combinatorics and Networking Lab, Moscow Institute of Physics and Technology (National Research University)
- Moscow Center for Fundamental and Applied Mathematics
- Moscow Institute of Physics and Technology (National Research University)
- Edição: Volume 212, Nº 4 (2021)
- Páginas: 76-90
- Seção: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133379
- DOI: https://doi.org/10.4213/sm9259
- ID: 133379
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Resumo
We investigate the problem of the most efficient first-order definition of the property of containing an induced subgraph isomorphic to a given pattern graph, which is closely related to the time complexity of the decision problem for this property.We derive a series of new bounds for the minimum quantifier depth of a formula defining this property for pattern graphs on five vertices, as well as for disjoint unions of isomorphic complete multipartite graphs. Moreover, we prove that for any $\ell\geq 4$ there exists a graph on $\ell$ vertices and a first-order formula of quantifier depth at most $\ell-1$ that defines the property of containing an induced subgraph isomorphic to this graph.Bibliography: 12 titles.
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Sobre autores
Maksim Zhukovskii
Advanced Combinatorics and Networking Lab, Moscow Institute of Physics and Technology (National Research University); Moscow Center for Fundamental and Applied Mathematics
Email: zhukmax@gmail.com
Doctor of physico-mathematical sciences
Eremei Kudryavtsev
Moscow Institute of Physics and Technology (National Research University)
Email: keremey57@gmail.com
Mikhail Makarov
Moscow Institute of Physics and Technology (National Research University)
Email: vbif-98@mail.ru
Aleksandra Shlychkova
Moscow Institute of Physics and Technology (National Research University)Bibliografia
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