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Reinforcement learning for graph theory, II. Small Ramsey numbers

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arxiv 2403.20055 v1 pith:ZGQRJP7W submitted 2024-03-29 math.CO

classification math.CO
keywords numbersramseysmallgraphlearninglowerreinforcementtheory
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abstract

We describe here how the recent Wagner's approach for applying reinforcement learning to construct examples in graph theory can be used in the search for critical graphs for small Ramsey numbers. We illustrate this application by providing lower bounds for the small Ramsey numbers $R(K_{2,5}, K_{3,5})$, $R(B_3, B_6)$ and $R(B_4, B_5)$ and by improving the lower known bound for $R(W_5, W_7)$.

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  1. Reinforcement learning for graph theory, Parallelizing Wagner's approach

    math.CO 2025-09 conditional novelty 4.0 of 10

    A parallelized RL search over graphs produces three new counterexamples to conjectured Laplacian spectral radius bounds, alongside a speedup claim that is only weakly supported.

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