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Graph quasivarieties

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Abstract

Introduced by C. R. Shallon in 1979, graph algebras establish a useful connection between graph theory and universal algebra. This makes it possible to investigate graph varieties and graph quasivarieties, i. e., classes of graphs described by identities or quasi-identities. In this paper, graph quasivarieties are characterized as classes of graphs closed under directed unions of isomorphic copies of finite strong pointed subproducts.

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References

  1. K. A. BAKER, G. F. MCNulty and H. WERNER, The finitely based varieties of graph algebras, Acta Sci. Math. (Szeged), 51 (1987) 3–15.

    MathSciNet  MATH  Google Scholar 

  2. C. BERGE, Färbung von Graphen, deren sämtliche bzw. deren ungerade Kreise starr sind (Zusammenfassung), Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe, 10 (1961) 114–115.

    Google Scholar 

  3. M. CHUDNOVSKY, N. ROBERTSON, P. SEYMOUR and R. THOMAS, The strong perfect graph theorem, Ann. of Math. (2), 164 (2006) 51–229.

    Article  MathSciNet  Google Scholar 

  4. E. W. KISS, A note on varieties of graph algebras, Universal algebra and lattice theory (Charleston, S. C., 1984), Lecture Notes in Math., 1149, C. D. Comer (ed.), Springer, Berlin, 1985, pp. 163–166.

    Chapter  Google Scholar 

  5. E. W. KISS, R. Pöschel and P. PRÖHLE, Subvarieties of varieties generated by graph algebras, ActaSci. Math. (Szeged), 54 (1990) 57–75.

    MathSciNet  MATH  Google Scholar 

  6. G. F. MCNULTY and C. R. SHALLON, Inherently nonfinitely based finite algebras, Universal Algebra and Lattice Theory (Puebla, 1982), Lecture Notes in Math., 1004, R. S. Freese and O. C. Garcia (eds.), Springer, Berlin, 1983, pp. 206–231.

    Google Scholar 

  7. R. Pöschel, Shallon-algebras and varieties for graphs and relational systems, Algebra und Graphentheorie, Jahrestagung Algebra und Grenzgebiete 28.10.–1.11.1985 in Siebenlehn (GDR), J. Machner and G. Schaar (eds.), Bergakademie Freiberg, Sektion Mathematik, 1986, pp. 53–56.

    Google Scholar 

  8. R. Pöschel, The equational logic for graph algebras, Z. Math. Logik Grundlag. Math., 35 (1989) 273–282.

    Article  MathSciNet  Google Scholar 

  9. R. Pöschel, Graph algebras and graph varieties, Algebra Universalis, 27 (1990) 559–577.

    Article  MathSciNet  Google Scholar 

  10. R. Pöschel and W. WESSEL, Classes of graphs definable by graph algebra identities or quasi-identities, Comment. Math. Univ. Carolin., 28 (1987) 581–592.

    MathSciNet  MATH  Google Scholar 

  11. C. R. SHALLON, Non-finitely based binary algebras derived from lattices, Ph. D. thesis, University of California, Los Angeles, 1979.

    Google Scholar 

  12. W. WECHLER, Universal Algebra for Computer Scientists, EATCS Monogr. Theoret. Comput. Sci. 25, Springer, Berlin, 1992.

    Google Scholar 

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Author notes

  1. Erkko Lehtonen

    Present address: Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829–516, Caparica, Portugal

Authors and Affiliations

  1. Institut für Algebra, Technische Universität Dresden, 01062, Dresden, Germany

    Erkko Lehtonen

  2. Institut für Algebra, Technische Universität Dresden, 01062, Dresden, Germany

    Reinhard Pöschel

Authors
  1. Erkko Lehtonen
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  2. Reinhard Pöschel
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Correspondence to Erkko Lehtonen.

Additional information

Communicated by L. Zádori

Acknowledgment.

The authors are thankful to the anonymous reviewer for a careful reading of our manuscript and for the useful suggestions that helped improve the presentation.

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Lehtonen, E., Pöschel, R. Graph quasivarieties. ActaSci.Math. 86, 31–50 (2020). https://doi.org/10.14232/actasm-019-528-9

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  • DOI: https://doi.org/10.14232/actasm-019-528-9

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