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CATEGORIES:Combinatorics Seminar
SUMMARY:Graphs with forbidden induced subgraphs - Alex Sco
tt (University of Oxford)
DTSTART;TZID=Europe/London:20200206T143000
DTEND;TZID=Europe/London:20200206T153000
UID:TALK138622AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/138622
DESCRIPTION:Ramsey's Theorem tells us that every graph on n ve
rtices contains a complete subgraph or independent
set of size about log n. Considering random grap
hs shows that this is all we can expect: for most
graphs\, the largest complete subgraph or independ
ent set has size O(log n). But what if we conside
r graphs G that do not contain some specific induc
ed subgraph H? Erdos and Hajnal\nconjectured in t
he 1980s that in this case G must have a complete
subgraph or independent set of size at least |G|^c
\, for some c=c(H). The Erdos-Hajnal conjecture r
emains open\, but we will discuss some recent prog
ress and related results. This talk includes join
t work with Maria Chudnovsky\, Jacob Fox\, Paul Se
ymour and Sophie Spirkl.\n\n
LOCATION:MR12
CONTACT:Andrew Thomason
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