Abstract
In this paper necessary and sufficient conditions are given for a generalized polyomino graph to have a perfect matching and to be elementary, respectively.
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Lovász, L., Plummer, M.D.: Matching Theory (Annals of Discrete Mathematics 29). Amsterdam: North-Holland, 1986
Plummer, M.D.: Matching Theory - a sampler: from Dénes Konig to the present. Discrete Math. 100, 177–219 (1992)
Propp, J.: Enumeration of Matchings: Problems and Progress, MSRI Publications Vol 38, Cambridge Univ. Press, 1999, pp. 255–291
Akiyama, J., Kano, M.: 1-factor of triangle graphs. In: Akiyama, J.: Number Theory and Combinatorics, World Scientific 1985, pp. 21–35
Zhang, H.P., Zhang, F.J.: Perfect matchings of polyomino graphs. Graphs and Combinatorics 13, 295–304 (1997)
Kostochka, A.V.: Proc. 30th Internat, Wiss, Koll TH Ilmenau. Vortragsreihe, E. 1985, pp. 49–52
Zhang, F.J., Guo, X.F., Chen, R.S.: Perfect matchings in hexagonal systems. Graphs and Combinatorics 1, 383–386 (1985)
Cyvin, S.J., Brunvoll, J., Cyvin, B.N., Chen, R.S., Zhang, F.J.: Theory of Coronoid Hydrocarbons II. Springer, Berlin Heidelberg, 1994
Kasteleyn, P.W.: The statistics of dimer on a lattice I., The number of dimer arrangement on a quadratic lattice. Physica 27, 1209–1225 (1961)
John, P., Sachs, H., Zerntic, H.: Counting perfect matchings in polyominoes with applications to the dimer problem. Zastosowania Matemetyki (Appl.math) 19, 465–477 (1987)
Sachs, H.: Counting perfect matchings in lattice graphs, In: Topics in combinatorics and graph theory, Heidelberg: Physica-Verlag 1990, pp. 577–584
Berge, C., Chen, C.C., Chvátal, V., Soaw, C.S.: Combinatorial properties of polyominoes. Combinatirica 1, 217–224 (1981)
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The project was supported financially by National Natural Science Foundation of China (10431020).
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Si, C. Perfect Matchings of Generalized Polyomino Graphs. Graphs and Combinatorics 21, 515–529 (2005). https://doi.org/10.1007/s00373-005-0624-1
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DOI: https://doi.org/10.1007/s00373-005-0624-1