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A Machine Learning Approach To Constructing Ramsey Graphs Leads To The Trahtenbrot-Zykov Problem., Emily Hawboldt
A Machine Learning Approach To Constructing Ramsey Graphs Leads To The Trahtenbrot-Zykov Problem., Emily Hawboldt
Electronic Theses and Dissertations
Attempts at approaching the well-known and difficult problem of constructing Ramsey graphs via machine learning lead to another difficult problem posed by Zykov in 1963 (now commonly referred to as the Trahtenbrot-Zykov problem): For which graphs F does there exist some graph G such that the neighborhood of every vertex in G induces a subgraph isomorphic to F? Chapter 1 provides a brief introduction to graph theory. Chapter 2 introduces Ramsey theory for graphs. Chapter 3 details a reinforcement learning implementation for Ramsey graph construction. The implementation is based on board game software, specifically the AlphaZero program and its …