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math.CO2026
Bipartite Extremal Numbers of Trees
Lucas Waite, Nuh Aydin
We study a restriction of the classical Erdős--Sós problem, the extremal number of trees, to the class of bipartite host graphs, both when only the order of the host is prescribed…
math.CO2026
Combinatorial Bounds for Codes over Metric Spaces: Ramsey-Sidorenko Thresholds and Subgraph Counts
Lucas Waite, Nuh Aydin
This paper investigates the relationship between coding theory and extremal combinatorics by representing codes in general metric spaces as independent sets in proximity graphs. We…