Tensor Networks and the Enumerative Geometry of Graphs

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Tensor Networks and the Enumerative Geometry of Graphs. / Zograf, P. G.

In: Journal of Mathematical Sciences (United States), Vol. 261, No. 5, 02.04.2022, p. 608-613.

Research output: Contribution to journal › Article › peer-review

Author

Zograf, P. G. / Tensor Networks and the Enumerative Geometry of Graphs. In: Journal of Mathematical Sciences (United States). 2022 ; Vol. 261, No. 5. pp. 608-613.

BibTeX

@article{49a7b4cc4d32484b959aefb115f7a4ad,

title = "Tensor Networks and the Enumerative Geometry of Graphs",

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 of proper edge colorings. We briefly discuss the computational complexity of the algorithms based on these formulas.",

author = "Zograf, {P. G.}",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = apr,

day = "2",

doi = "10.1007/s10958-022-05775-2",

language = "English",

volume = "261",

pages = "608--613",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Tensor Networks and the Enumerative Geometry of Graphs

AU - Zograf, P. G.

PY - 2022/4/2

Y1 - 2022/4/2

N2 - 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.

AB - 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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UR - https://www.mendeley.com/catalogue/7e90352f-5c67-3204-9e05-3e295fff17d1/

U2 - 10.1007/s10958-022-05775-2

DO - 10.1007/s10958-022-05775-2

M3 - Article

AN - SCOPUS:85127551275

VL - 261

SP - 608

EP - 613

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 98426680