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Zapiski Nauchnykh Seminarov POMI, 2021, Volume 507, Pages 26–34 (Mi znsl7159)  

Tensor networks and the enumerative geometry of graphs

P. G. Zografab

a St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia
b Chebyshev Laboratory, St. Petersburg State University, St. Petersburg, Russia
References:
Abstract: 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 proper edge colorings. We briefly discuss the problem of the computational complexity of the algorithms based on these formulas.
Key words and phrases: tensor network, $d$-regular subgraph, $d$-factor, edge coloring.
Funding agency Grant number
Russian Science Foundation 21-11-00040
This work was supported by the Russian Science Foundation grant 21-11-00040.
Received: 18.11.2021
Document Type: Article
UDC: 519.17
Language: English
Citation: P. G. Zograf, “Tensor networks and the enumerative geometry of graphs”, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Zap. Nauchn. Sem. POMI, 507, POMI, St. Petersburg, 2021, 26–34
Citation in format AMSBIB
\Bibitem{Zog21}
\by P.~G.~Zograf
\paper Tensor networks and the enumerative geometry of graphs
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXXIII
\serial Zap. Nauchn. Sem. POMI
\yr 2021
\vol 507
\pages 26--34
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7159}
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  • https://www.mathnet.ru/eng/znsl/v507/p26
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