On the optimality of the Arf invariant formula for graph polynomials
Martin Loebl, Gregor Masbaum
TL;DR
This paper proves that the Arf invariant formula is optimal for computing the generating function of even subgraphs and the Ising partition function in graphs, establishing its theoretical limits.
Contribution
It establishes the optimality of the Arf invariant formula for graph polynomials related to the Ising model.
Findings
Proves the Arf invariant formula's optimality for the Ising partition function.
Clarifies the theoretical limits of the Arf invariant approach.
Provides a rigorous mathematical validation of the formula's optimality.
Abstract
We prove optimality of the Arf invariant formula for the generating function of even subgraphs, or, equivalently, the Ising partition function, of a graph.
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