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Tensor Networks and the Enumerative Geometry of Graphs

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We propose a universal approach to a range of enumeration problems in graphs by means of tensor networks. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. This approach leads to simple formulas that count, in particular, the number of d-regular subgraphs of an arbitrary graph (including the number of d-factors) and of proper edge colorings. We briefly discuss the computational complexity of the algorithms based on these formulas.

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Authors and Affiliations

  1. St.Petersburg Department of Steklov Institute of Mathematics and Chebyshev Laboratory, St.Petersburg State University, St. Petersburg, Russia

    P. G. Zograf

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  1. P. G. Zograf
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Correspondence to P. G. Zograf.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 507, 2021, pp. 26–34.

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Zograf, P.G. Tensor Networks and the Enumerative Geometry of Graphs. J Math Sci 261, 608–613 (2022). https://doi.org/10.1007/s10958-022-05775-2

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  • DOI: https://doi.org/10.1007/s10958-022-05775-2

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