New Results for Some Turán Problem Instances Obtained Using the Reinforcement Learning Technique

The Turán number ex(n, F) represents the maximum number of edges in an F-free graph on n vertices. Determining these numbers for general graphs is a long-standing and challenging open problem. Ideally, one aims not only to compute these numbers exactly but also to understand their asymptotic behavior, although such results are currently limited to specific cases. This article introduces new results for \(ex(n,C_{2k})\) and the associated parameter f(n, 2k), achieved through the application of reinforcement machine learning techniques. Specifically, the RLS algorithm, initially proposed by Zhou et al. for vertex coloring in graphs, has been adapted to address certain Turán problems involving edge coloring.