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\(\mathcal{Q}\)-Universal Quasivarieties of Graphs

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It is proved that a quasivariety K of undirected graphs without loops is \(\mathcal{Q}\)-universal if and only if K contains some non-bipartite graph.

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REFERENCES

  1. M. Sapir, “The lattice of quasivarieties of semigroups,” Alg. Univ., 21, No. 2, 172-180 (1985).

    Google Scholar 

  2. S. V. Sizyi, “Quasivarieties of graphs,” Sib. Mat. Zh., 35, No. 4, 879-892 (1994).

    Google Scholar 

  3. M. E. Adams and W. Dziobiak, “Q-universal quasivarieties of algebras,” Proc. Am. Math. Soc., 120, No. 4, 1053-1059 (1994).

    Google Scholar 

  4. V. A. Gorbunov, “Structure of lattices of varieties and lattices of quasivarieties: similarity and difference. II,” Algebra Logika, 34, No. 4, 369-397 (1995).

    Google Scholar 

  5. V. A. Gorbunov, Algebraic Theory of Quasivarieties [in Russian], Nauch. Kniga, Novosibirsk (1999).

    Google Scholar 

  6. M. E. Adams and W. Dziobiak, “Finite-to-.nite universal quasivarieties are Q-universal, Alg. Univ., 46, Nos. 1/2, 253-283 (2001).

    Google Scholar 

  7. M. E. Adams and W. Dziobiak, “The lattice of quasivarieties of undirected graphs,” Alg. Univ., 47, No. 1, 7-11 (2002).

    Google Scholar 

  8. A. Pultr and V. Trnková, Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, Academia, Prague (1980).

    Google Scholar 

  9. V. I. Tumanov, “Quasivarieties of lattices,” in XVI All-Union Conference on Algebra, Vol. 2, Leningrad (1981), p. 135.

    Google Scholar 

  10. W. Dziobiak, “On lattice identities satisfied in subquasivariety lattices of varieties of modular lattices,” Alg. Univ., 22, No. 2, 205-214 (1986).

    Google Scholar 

  11. M. P. Tropin, “Embedding a free lattice in the lattice of quasivarieties of distributive lattices with pseudocomplementation,” Algebra Logika, 22, No. 2, 159-167 (1983).

    Google Scholar 

  12. G. Grätzer and H. Lakser, “A note on the implicational class generated by a class of structures,” Can. Math. Bull., 16, No. 4, 603-605 (1973).

    Google Scholar 

  13. A. V. Kravchenko, “The lattice complexity of quasivarieties of graphs and endographs,” Algebra Logika, 36, No. 3, 273-281 (1997).

    Google Scholar 

  14. Z. Hedrlín and A. Pultr, “Symmetric relations (undirected graphs) with given semigroups,” Monatsh. Math., 69, No. 4, 318-324 (1965).

    Google Scholar 

  15. V. A. Gorbunov and A. V. Kravchenko, “Universal Horn classes and colour-families of graphs,” Preprint No. 1957, Technische Universität Darmstadt, Darmstadt (1997).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Akademika Koptyuga Prospekt, Novosibirsk, 630090

    A. V. Kravchenko

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  1. A. V. Kravchenko
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Kravchenko, A.V. \(\mathcal{Q}\)-Universal Quasivarieties of Graphs. Algebra and Logic 41, 173–181 (2002). https://doi.org/10.1023/A:1016024925028

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