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Tensor networks and the enumeration of regular subgraphs

Peter Zograf
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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.

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Peter Zograf. 2006-05-10. Tensor networks and the enumeration of regular subgraphs. https://arxiv.org/abs/math/0605256

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