Correlation between residual entropy and spanning tree entropy of ice-type models on graphs
Combinatorics
2025-03-07 v2 Mathematical Physics
math.MP
Abstract
The logarithm of the number of Eulerian orientations, normalised by the number of vertices, is known as the residual entropy in studies of ice-type models on graphs. The spanning tree entropy depends similarly on the number of spanning trees. We demonstrate and investigate a remarkably strong, though non-deterministic, correlation between these two entropies. This leads us to propose a new heuristic estimate for the residual entropy of regular graphs that performs much better than previous heuristics. We also study the expansion properties and residual entropy of random graphs with given degrees.
Cite
@article{arxiv.2409.04989,
title = {Correlation between residual entropy and spanning tree entropy of ice-type models on graphs},
author = {Mikhail Isaev and Brendan D. McKay and Rui-Ray Zhang},
journal= {arXiv preprint arXiv:2409.04989},
year = {2025}
}
Comments
Corollary 2.7 is improved, extensive rearrangements, new data