Extremal Theory

How many edges can we keep in a graph while avoiding a prescribed configuration? My work focuses on this question in Hamming graphs, which provide a setting for connecting classical extremal graph theory with extremal problems in the hypercube.

Current Work

• Turán Densities in Hamming Graphs — Manuscript in preparation, developing questions from my master’s research.
• Extremal Problems on Hamming Graphs — My master’s thesis.

Planned Background Articles

• Turán Theory — Forbidden subgraphs, extremal numbers, and edge densities: the classical questions motivating the Hamming graph setting.
• Extremal Problems in Hypercubes — The structure of the hypercube and how its growing dimension shapes forbidden-subgraph problems.
• Hamming Graphs — Cartesian products of complete graphs, the roles of alphabet size and dimension, and the connection between classical and hypercube extremal theory.
• Computational Methods for Extremal Densities — Using finite examples, computational experiments, and flag algebra methods to investigate constructions and bounds relevant to this project.