#
The Most Wanted Folkman Number

##
Christopher Wood

In this talk we discuss a branch of Ramsey theory concerning edge
Folkman numbers, as well as several computational techniques that
have been used to solve problems therein. The edge Folkman number
Fe(s,t;q) is the order of the smallest Kq-free graph G such that G ->
(s,t)^e, where G->(s,t)^e is true iff for all red and blue edge
colorings of G there exists a monochromatic Ks or Kt. Our main focus
is on the edge Folkman number Fe(3,3;4). We present relevant
background for this particular problem, survey related work and
computational techniques for computing Folkman numbers, and finally,
discuss ongoing work attempting to prove that the Fe(3,3;4) <= 127.