Geodesic
Tensor networks and the enumerative geometry of graphs
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 26-34

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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 proper edge colorings. We briefly discuss the problem of the computational complexity of the algorithms based on these formulas. 
@article{ZNSL_2021_507_a2,
     author = {P. G. Zograf},
     title = {Tensor networks and the enumerative geometry of graphs},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {26--34},
     publisher = {mathdoc},
     volume = {507},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a2/}
}
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P. G. Zograf. Tensor networks and the enumerative geometry of graphs. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 26-34. http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a2/