# Refutation of Spectral Graph Theory Conjectures with Monte Carlo Search

arXiv: https://arxiv.org/abs/2207.03343 · HTML: https://mlsanity.com/paper/2207.03343/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 28 references that are in the map.
- First posted on arXiv 4 Jul 2022.

## Builds on (most cited first, 1 of 1)

- [Constructions in combinatorics via neural networks](https://mlsanity.com/paper/2104.14516/) (2021)

## Built on by (most cited first, 4 of 4)

- [Learning to Disprove: Formal Counterexample Generation with Large Language Models](https://mlsanity.com/paper/2603.19514/) (2026)
- [Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?](https://mlsanity.com/paper/2501.18527/) (2025)
- [Adaptive Monte Carlo Search for Conjecture Refutation in Graph Theory](https://mlsanity.com/paper/2306.07956/) (2023)
- [Refutation of Spectral Graph Theory Conjectures with Search Algorithms)](https://mlsanity.com/paper/2409.18626/) (2024)

## Abstract (arXiv)

We demonstrate how Monte Carlo Search (MCS) algorithms, namely Nested Monte Carlo Search (NMCS) and Nested Rollout Policy Adaptation (NRPA), can be used to build graphs and find counter-examples to spectral graph theory conjectures in minutes.