Refutation of Spectral Graph Theory Conjectures with Monte Carlo Search
Milo Roucairol, Tristan Cazenave
TL;DR
This paper showcases how Monte Carlo Search algorithms can rapidly construct graphs and identify counter-examples to spectral graph theory conjectures, challenging existing assumptions efficiently.
Contribution
It introduces the application of NMCS and NRPA algorithms for graph construction and conjecture refutation in spectral graph theory.
Findings
MCS algorithms can generate graphs in minutes
Counter-examples to spectral graph conjectures are found using MCS
The approach is efficient and effective for testing conjectures
Abstract
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.
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Taxonomy
TopicsComplex Network Analysis Techniques · Advanced Database Systems and Queries · Graph Theory and Algorithms