Description
In 2020, Coregliano and Razborov introduced a general
framework to study limits of combinatorial objects, using logic and
model theory. They introduced the abstract chromatic number and
proved/reproved multiple Erdős-Stone-Simonovits-type theorems in
different settings. In 2022, Coregliano extended this by showing that
similar results hold when we count copies of $K_t$ instead of edges.
Our aim is threefold. First, we provide a purely combinatorial
approach. Second, we extend their results by showing several other graph
parameters and other settings where Erdős-Stone-Simonovits-type
theorems follow. Third, we go beyond determining asymptotics and obtain
corresponding stability, supersaturation, and sometimes even exact
results.
Joint work with Hilal Hama Karim and Gaurav Kucheriya