New Graph and Hypergraph Container Lemmas with Applications in Property Testing

The graph and hypergraph container methods are powerful tools with a wide range of applications across combinatorics. Recently, Blais and Seth (FOCS 2023) showed that the graph container method is particularly well-suited for the analysis of the natural canonical tester for two fundamental graph properties: having a large independent set and k-colorability. In this work, we show that the connection between the container method and property testing extends further along two different directions.