Recent work on the Erdos-Hajnal Conjecture

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• Alex Scott (University of Oxford)
• Wednesday 10 April 2024, 10:00-11:00
• Seminar Room 1, Newton Institute.

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OOEW04 - Structure and Randomness - a celebration of the mathematics of Timothy Gowers

A typical graph contains cliques and independent sets of no more than logarithmic size.  The Erdos-Hajnal Conjecture asserts that if we forbid some induced subgraph H then we can do much better: the conjecture claims that there is some c=c(H)>0 such that every H-free graph G contains a clique or independent set of size at least |G|^c.  The conjecture looks far out of reach, and is only known for a small family of graphs.  We will discuss some recent progress. Joint work with Tung Nguyen and Paul Seymour.

This talk is part of the Isaac Newton Institute Seminar Series series.

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