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SUMMARY:Chaya Keller (Ariel University)
DTSTART:20210527T140000Z
DTEND:20210527T160000Z
DTSTAMP:20260422T065715Z
UID:CJCS/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/20/">On
  multicolor Ramsey numbers and subset-coloring of hypergraphs</a>\nby Chay
 a Keller (Ariel University) as part of Copenhagen-Jerusalem Combinatorics 
 Seminar\n\n\nAbstract\nThe multicolor hypergraph Ramsey number R_k(s\,r) i
 s the minimal n\, such that in any k-coloring of all r-element subsets of 
 [n]\, there is a subset of size s\, all whose r-subsets are monochromatic.
  We present a new "stepping-up lemma" for R_k(s\,r):  If R_k(s\,r)>n\, the
 n R_{k+3}(s+1\,r+1)>2^n. Using the lemma\, we improve some known lower bou
 nds on multicolor hypergraph Ramsey numbers.\nFurthermore\, given a hyperg
 raph H=(V\,E)\, we consider the Ramsey-like problem of coloring all r-subs
 ets of V such that no hyperedge of size >r is monochromatic. We provide up
 per and lower bounds on the number of colors necessary in terms of the chr
 omatic number \\chi(H). In particular\, we show that this number is O(log^
 {(r-1)} (r \\chi(H)) + r)\, where log^{(m)} denotes m-fold logarithm.\n\nJ
 oint work with Bruno Jartoux\, Shakhar Smorodinsky\, and Yelena Yuditsky.\
 n
LOCATION:https://researchseminars.org/talk/CJCS/20/
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