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SUMMARY:Induced subgraphs of induced subgraphs of large chromatic number -
  Alexander Scott (Oxford)
DTSTART:20221110T143000Z
DTEND:20221110T153000Z
UID:TALK192491@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:We prove that\, for every graph F\, there is a constant c=c(F)
  and a graph G of\ninfinite chromatic number in which every induced subgra
 ph of chromatic number\nat least c contains an induced subgraph isomorphic
  to F. Furthermore\, if F has\nclique number k>1 then we can take G to hav
 e clique number k as well. This\ngeneralises recent theorems of Briański\
 , Davies and Walczak\, and of Carbonero\,\nHompe\, Moore and Spirkl. Our r
 esults show that\, for every F \, the class of\nF-free graphs satisfy a ve
 ry strong Ramsey-type property\, giving a very strong\ngeneralisation of a
  result of Folkman from 1970. We also prove an analogous\nstatement where 
 clique number is replaced by odd girth.\n\nJoint work with António Girão
 \, Freddie Illingworth\, Emil Powierski\, Michael\nSavery\, Youri Tamitega
 ma and Jane Tan.
LOCATION:MR12
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