A conjecture on independent sets and graph covers

TL;DR

This paper proposes a conjecture relating the number of independent sets in graph covers to the partition function of binary attractive models, suggesting the Bethe approximation underestimates the true partition function.

Contribution

Introduces a new conjecture connecting independent sets in graph covers with the accuracy of the Bethe approximation for binary models.

Findings

Conjecture links independent sets to partition functions.

Implication that Bethe approximation underestimates the true value.

Provides a theoretical basis for improved approximation methods.

Abstract

In this article, I present a conjecture on the number of independent sets on graph covers. I also show that the conjecture implies that the partition function of a binary pairwise attractive model is greater than that of the Bethe approximation.