Work

Correlation between residual entropy and spanning tree entropy of ice-type models on graphs

Year: 2025

Type: article

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.

Source: Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions

DOI: 10.4171/aihpd/207

Authors: Mikhail Isaev, Brendan D. McKay, Rui-Ray Zhang

Institutions: UNSW Sydney, Australian National University

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408810086

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