English

Tensor networks and the enumeration of regular subgraphs

Combinatorics 2007-05-23 v1

Abstract

We propose a universal approach to a range of enumeration problems in graphs. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. In particular, this leads to an algorithm that counts the number of d-regular subgraphs of an arbitrary graph including the number of d-factors (previously we considered the case d=2 with a special emphasis on the enumeration of Hamiltonian cycles; cf. math.CO/0403339). We briefly discuss the problem of the computational complexity of this algorithm.

Keywords

Cite

@article{arxiv.math/0605256,
  title  = {Tensor networks and the enumeration of regular subgraphs},
  author = {Peter Zograf},
  journal= {arXiv preprint arXiv:math/0605256},
  year   = {2007}
}
R2 v1 2026-07-22T17:35:37.182Z