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On an extremal inverse problem in graph theory

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Abstract

We consider the problem of constructing a graph having some given number of independent sets. The bounds are obtained for the number of vertices in bipartite graphs with the prescribed number of independent sets and the number of inclusion maximal independent sets.

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References

  1. É. Czabarka, L. Székely, and S. Wagner, “The Inverse Problem for Certain Tree Parameters,” Discrete Appl. Math. 157(15), 3314–3319 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Erdös and T. Gallai, “Gráfok előírt fokú pontokkal,” Mat. Lapok. 11, 264–274 (1960).

    Google Scholar 

  3. V. Havel, “Poznámka o existenci konečných grafů,” Časopis pro pěstování matematiky 80(4), 477–480 (1955).

    MATH  MathSciNet  Google Scholar 

  4. V. Linek, “Bipartite Graphs Can Have Any Number of Independent Sets,” Discrete Math. 76(2), 131–136 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Wagner, “A Class of Trees and Its Wiener Index,” Acta Appl. Math. 91(2), 119–132 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  6. H. Wang and G. Yu, “All but 49 Numbers Are Wiener Indices of Trees,” Acta Appl. Math. 92(1), 15–20 (2006).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700, Russia

    A. B. Dainyak & A. D. Kurnosov

Authors
  1. A. B. Dainyak
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  2. A. D. Kurnosov
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Correspondence to A. B. Dainyak.

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Original Russian Text © A.B. Dainyak, A.D. Kurnosov, 2015, published in Diskretnyi Analiz i Issledovanie Operatsii, 2015, Vol. 22, No. 1, pp. 19–30.

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Dainyak, A.B., Kurnosov, A.D. On an extremal inverse problem in graph theory. J. Appl. Ind. Math. 9, 157–164 (2015). https://doi.org/10.1134/S1990478915020027

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  • DOI: https://doi.org/10.1134/S1990478915020027

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