Reinforcement learning for graph theory, I. Reimplementation of Wagner's approach

TL;DR

This paper reimplements Wagner's reinforcement learning approach for graph theory, enhancing readability, stability, and speed, and demonstrates its effectiveness by constructing counterexamples for conjectured bounds on the Laplacian spectral radius.

Contribution

It provides a reimplementation of Wagner's method, improving its usability and applying it to generate counterexamples for key graph theory conjectures.

Findings

Enhanced algorithm stability and speed

Successful construction of counterexamples for conjectured bounds

Demonstrated applicability to spectral graph theory

Abstract

We reimplement here the recent approach of Adam Zsolt Wagner [arXiv:2104.14516], which applies reinforcement learning to construct (counter)examples in graph theory, in order to make it more readable, more stable and much faster. The presented concepts are illustrated by constructing counterexamples for a number of published conjectured bounds for the Laplacian spectral radius of graphs.