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Induced subgraphs of F-free graphs

Introductory Workshop - Graph Theory: Extremal, Probabilistic and Structural February 10, 2025 - February 14, 2025

February 12, 2025 (09:30 AM PST - 10:15 AM PST)
Speaker(s): Jacques Verstraete (University of California, San Diego)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Induced subgraphs of F-free graphs

Abstract

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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

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Induced subgraphs of F-free graphs

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