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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20261005T150000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/graphs-and-m
 atroids-jun-yan-ramsey-numbers-trees
SUMMARY:Graphs and Matroids | Jun Yan\, Ramsey numbers of trees
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n Jun Yan\n\nAFFILIATION:\n University of Waterloo\n\n
 ROOM:\n MC 6029\n\nABSTRACT: Let T be a tree with bipartition class sizes
  t_1>=t_2.\nMotivated by two simple lower bound constructions\, Burr conje
 ctured\nthat the Ramsey number of T\, denoted by R(T)\, is exactly\nmax{t_
 1+2t_2\,2t_1}-1. While this conjecture turns out to be false\, all\nknown 
 counterexamples have large maximum degrees. In a joint work with\nRichard 
 Montgomery and Matías Pavez-Signé\, we show that there exists\na constan
 t c>0\, such that Burr's conjecture does hold if T has maximum\ndegree at 
 most c(t_1+t_2). In particular\, this determines the exact\nRamsey numbers
  of a large family of trees. In this talk\, I will go\nover some backgroun
 d on tree embeddings\, and give an overview of our\nproof. 
DTSTAMP:20261003T212200Z
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