Research output: Contribution to journal › Article › peer-review
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
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TY - JOUR
T1 - Tensor Networks and the Enumerative Geometry of Graphs
AU - Zograf, P. G.
N1 - Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
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.
UR - http://www.scopus.com/inward/record.url?scp=85127551275&partnerID=8YFLogxK
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