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Title: | The proof of the perepechko's conjecture concerning near-perfect matchings on C<inf>m</inf> x P<inf>n</inf> cylinders of odd order | Authors: | Doroslovački Rade Đokić Jelena Pantić Bojana Bodroža-Pantić Olga |
Issue Date: | 2019 | Journal: | Applicable Analysis and Discrete Mathematics | Abstract: | © 2019 University of Belgrade. For all odd values of m, we prove that the sequence of the numbers of near-perfect matchings on Cm x P2n+1 cylinder with a vacancy on the boundary obeys the same recurrence relation as the sequence of the numbers of perfect matchings on Cm x P2n. Further more, we prove that for all odd values of m denominator of the generating function for the total number of the near-perfect matchings on Cm x P2n+1 graph is always the square of denominator of generating function for the sequence of the numbers of perfect matchings on Cm x P2n graph, as recently conjectured by Perepechko. | URI: | https://open.uns.ac.rs/handle/123456789/20156 | ISSN: | 1452-8630 | DOI: | 10.2298/AADM181016002D |
Appears in Collections: | PMF Publikacije/Publications |
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