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Perfect Matchings in Bipartite Lattice Animals: Lower Bounds and Realizability

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Abstract

In the first part of this paper we establish sharp lower bounds on the number of perfect matchings in benzenoid graphs and polyominoes. The results are then used to determine which integers can appear as the number of perfect matchings of infinitely many benzenoids and/or polyominoes. Finally, we consider the problem of concealed non-Kekuléan polyominoes. It is shown that the smallest such polyomino has 15 squares, and that such polyominoes on n squares exist for all n ≥ 15.

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References

  1. W.C. Shiu P.C.B. Lam F. Zhang H. Zhang (2002) J. Math. Chem. 31 405 Occurrence Handle10.1023/A:1021072722165 Occurrence HandleMR1959607

    Article  MathSciNet  Google Scholar 

  2. P.C.B. Lam W.C. Shiu H. Zhang (2003) MATCH 49 127

    Google Scholar 

  3. T. Došlić (2005) Croat Chem. Acta 78 25

    Google Scholar 

  4. L. Lovasz M.D. Plummer (1986) Matching Theory North-Holland Amsterdam, The Netherlands

    Google Scholar 

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

    Google Scholar 

  6. D.B. West (1996) Introduction to Graph Theory Prentice Hall Upper Saddle River, NJ

    Google Scholar 

  7. S.J. Cyvin I. Gutman (1988) Kekulé Structures in Benzenoid Hydrocarbons Springer Heidelberg

    Google Scholar 

  8. C. Rongsi S.J. Cyvin J. Brunvoll D.J. Klein (1990) Topics Curr. Chem. 153 227

    Google Scholar 

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Authors and Affiliations

  1. Department of Informatics and Mathematics, Faculty of Agriculture, University of Zagreb, Svetošimunska c. 25, 10000, Zagreb, CROATIA

    Tomislav Došlić

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  1. Tomislav Došlić
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Correspondence to Tomislav Došlić.

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Došlić, T. Perfect Matchings in Bipartite Lattice Animals: Lower Bounds and Realizability. J Math Chem 38, 617–627 (2005). https://doi.org/10.1007/s10910-005-6915-1

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  • DOI: https://doi.org/10.1007/s10910-005-6915-1

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