Refutation of Spectral Graph Theory Conjectures with Search Algorithms)
This work addresses the challenge of efficiently disproving graph theory conjectures for researchers in mathematics and computer science, representing an incremental improvement over existing methods.
The authors tackled the problem of automatically refuting spectral graph theory conjectures by using search algorithms to find large counter-examples quickly, refuting 12 out of 13 previously refuted conjectures in seconds and also refuting an open conjecture (197 from Graffiti).
We are interested in the automatic refutation of spectral graph theory conjectures. Most existing works address this problem either with the exhaustive generation of graphs with a limited size or with deep reinforcement learning. Exhaustive generation is limited by the size of the generated graphs and deep reinforcement learning takes hours or days to refute a conjecture. We propose to use search algorithms to address these shortcomings to find potentially large counter-examples to spectral graph theory conjectures in seconds. We apply a wide range of search algorithms to a selection of conjectures from Graffiti. Out of 13 already refuted conjectures from Graffiti, our algorithms are able to refute 12 in seconds. We also refute conjecture 197 from Graffiti which was open until now.