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SUMMARY:Recent work on the Erdos-Hajnal Conjecture - Alex Scott (Universit
 y of Oxford)
DTSTART:20240410T090000Z
DTEND:20240410T100000Z
UID:TALK213967@talks.cam.ac.uk
DESCRIPTION:A typical graph contains cliques and independent sets of no mo
 re than logarithmic size.&nbsp\; The Erdos-Hajnal Conjecture asserts that 
 if we forbid some induced subgraph H then we can do much better: the conje
 cture claims that there is some c=c(H)>0 such that every H-free graph G co
 ntains a clique or independent set of size at least |G|^c.&nbsp\; The conj
 ecture looks far out of reach\, and is only known for a small family of gr
 aphs.&nbsp\; We will discuss&nbsp\;some recent progress.\nJoint work with 
 Tung Nguyen and Paul Seymour.
LOCATION:Seminar Room 1\, Newton Institute
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