Induced subgraphs of F-free graphs
Introductory Workshop - Graph Theory: Extremal, Probabilistic and Structural February 10, 2025 - February 14, 2025
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
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Induced subgraphs of F-free graphs
Given graphs F and G, the Erdos-Rogers function asks for the largest number of vertices in an F-free induced subgraph of every n-vertex G-free graph. These are generalizations of Ramsey numbers, and have been extensively researched in the literature. A key part of estimating these quantities is the same question in graphs of prescribed maximum degree. In this talk, we show that this quantity has two principal regimes, according as G is a subgraph of a blowup of F or not, and we use this result to give new bounds on Erdos-Rogers functions.
Joint work with D. Mubayi and P. Morawski
Induced subgraphs of F-free graphs
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