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Pfaffian polyominos on the Klein bottle

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Abstract

If a graph G is Pfaffian, then the number of perfect matchings of G can be computed in polynomial time. So it makes sense to test whether a graph is Pfaffian. Historically in organic chemistry and combinatorial mathematics, polyominos have attracted the most attention. In this paper, we characterize all Pfaffian polyominos on the Klein bottle.

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Acknowledgements

This work is supported by the Institute of Meteorological Big Data-Digital Fujian and Fujian Key Laboratory of Data Science and Statistics.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, 363000, Fujiang, People’s Republic of China

    Yan Wang

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  1. Yan Wang
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Correspondence to Yan Wang.

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Partially supported by NSF of China (No.11671186); NSF of Fujian Province (2017J01404); Science Foundation for the Education Department of Fujian Province (JZ160455)

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Wang, Y. Pfaffian polyominos on the Klein bottle. J Math Chem 56, 3147–3160 (2018). https://doi.org/10.1007/s10910-018-0938-x

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