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Lattice complete graphs

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Abstract

We study the properties of graphs that can be placed in a rectangular lattice so that all vertices located in the same (horizontal or vertical) row be adjacent. Some criterion is formulated for an arbitrary graph to be in the specified class.

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References

  1. Yu. E. Bessonov, “On the Solution to the Greatest Intersection Search Problem on Graphs with the Use of Analysis of Subgraph Projections in the Modular Product of the Graphs,” in Computing Systems, Vol. 112 (Inst.Mat., Novosibirsk, 1985), pp. 3–22.

    Google Scholar 

  2. Yu. E. Bessonov, Using the Properties of Lattice Complete Graphs for Search of Common Substructures, Available from VINITI RAN 03.02.2014, No. 32-B2014 (Moscow, 2014).

    Google Scholar 

  3. Yu. E. Bessonov, Using the Properties of Lattice Complete Graphs for Analysis of Structure Symmetries, Available from VINITI RAN 10.06.2014, No. 169-B2014 (Moscow, 2014).

    Google Scholar 

  4. Yu. E. Bessonov, G. L. Mishchenko, and V. A. Skorobogatov, “On the Problem of Determining Skeleton Schemes of Chemical Reactions under Construction of Information Systems in Chemistry,” Nauchno-Tekh. Inform. Ser. 2, 1, 8–12 (1985).

    Google Scholar 

  5. V. G. Vizing, “Reduction of the Isomorphism and Isomorphic Embedding Problems to the Evaluation Problem for Nondensity of a Graph,” in Proceedings of III All-Union Conference on Problems of Theoretical Cybernetics (Inst. Mat., Novosibirsk, 1974), p. 124.

    Google Scholar 

  6. N. G. Zagoruiko, V. A. Skorobogatov, and P. V. Khvorostov, “Topics in the Analysis and Recognition of Molecular Structures on the Basis of Studying the Common Fragments,” in Computing Systems, Vol. 103 (Inst.Mat., Novosibirsk, 1984), pp. 26–50.

    MATH  Google Scholar 

  7. T. Akutsu, “A Polynomial Time Algorithm for Finding a Largest Common Subgraph of Almost Trees of Bounded Degree,” IEICE Trans. Fundamentals E76-A (9), 1488–1493 (1993).

    Google Scholar 

  8. H. G. Barrow and R. M. Burstall, “Subgraph Isomorphism, Matching Relational Structures and Maximal Cliques,” Inform. Proc. Lett. 4 (4), 83–84 (1976).

    Article  MATH  Google Scholar 

  9. V. Bonnici, R. Giugno, A. Pulvirenti, D. Shasha, and A. Ferro, “A Subgraph Isomorphism Algorithm and Its Application to Biochemical Data,” BMC Bioinform. 14 (Suppl. 7), S13, 1–13 (2013).

    Google Scholar 

  10. E. Duesbury, J. D. Holliday, and P. Willett, “Maximum Common Subgraph Isomorphism Algorithms,” MATCH Commun. Math. Comput. Chem. 77, 213–232 (2017).

    MathSciNet  Google Scholar 

  11. H. C. Ehrlich and M. Rarey, “Maximum Common Subgraph Isomorphism Algorithms and Their Applications inMolecular Science: A Review,” WIREs Comput. Molecular Sci. 1, 68–79 (2011).

    Article  Google Scholar 

  12. H. Fröhlich, A. Košir, and B. Zajc, “Optimization of FPGA Configurations Using Parallel Genetic Algorithm,” Inform. Sci. 133 (3), 195–219 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  13. N. Funabiki and J. Kitamichi, “A Two-Stage Discrete Optimization Method for Largest Common Subgraph Problems,” IEICE Trans. Inform. Syst. E82-D (8), 1145–1153 (1999).

    Google Scholar 

  14. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979; Mir,Moscow, 1982).

    MATH  Google Scholar 

  15. M. Grötschel, L. Lovász, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization (Springer, Heidelberg, 1988).

    Book  MATH  Google Scholar 

  16. F. Harary, Graph Theory (Addison-Wesley, Reading,MA, 1969).

    Book  MATH  Google Scholar 

  17. J. E. Hopcroft and R.M. Karp, “An n 5/2 Algorithm for Maximum Matchings in Bipartite Graphs,” SIAM J. Comput. 2 (4), 225–231 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  18. G. Levi, “A Note on the Derivation of Maximal Common Subgraphs of Two Directed or Undirected Graphs,” Calcolo 9 (4), 341–352 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  19. J. J. McGregor, “Backtrack Search Algorithms and the Maximal Common Subgraph Problem,” Software Pract. Exper. 12, 23–34 (1982).

    Article  MATH  Google Scholar 

  20. J.W. Raymond, E. J. Gardiner, and P. Willett, “Heuristics for Similarity Searching of ChemicalGraphsUsing aMaximum Common Edge Subgraph Algorithm,” J. Chem. Inform. Comput. Sci. 42 (2), 305–316 (2002).

    Article  Google Scholar 

  21. J.W. Raymond and P. Willett, “Maximum Common Subgraph Isomorphism Algorithms for the Matching of Chemical Structures,” J. Comput. Aided Molecular Design 16, 521–533 (2002).

    Article  Google Scholar 

  22. J. R. Ullmann, “An Algorithm for Subgraph Isomorphism,” J. ACM 16, 31–42 (1976).

    Article  MathSciNet  Google Scholar 

  23. M. Wagener and J. Gasteiger, “The Determination of Maximum Common Substructures by a Genetic Algorithm: Application in Synthesis Design and for the Structural Analysis of Biological Activity,” Angew. Chem. Intern. Ed. Engl. 33 (11), 1189–1192 (1994).

    Article  Google Scholar 

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Authors and Affiliations

  1. All-Russian Institute of Scientific and Technical Information, ul. Usievicha 20, Moscow, 125190, Russia

    Yu. E. Bessonov

  2. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. A. Dobrynin

Authors
  1. Yu. E. Bessonov
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  2. A. A. Dobrynin
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Corresponding author

Correspondence to Yu. E. Bessonov.

Additional information

Original Russian Text © Yu.E. Bessonov, A.A. Dobrynin, 2017, published in Diskretnyi Analiz i Issledovanie Operatsii, 2017, Vol. 24, No. 4, pp. 22–33.

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Bessonov, Y.E., Dobrynin, A.A. Lattice complete graphs. J. Appl. Ind. Math. 11, 481–485 (2017). https://doi.org/10.1134/S1990478917040032

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  • DOI: https://doi.org/10.1134/S1990478917040032

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