Computing the Folkman number F_v(2,2,3;4)

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Title: Computing the Folkman number F_v(2,2,3;4)
Author: Coles, Jonathan; Radziszowski, Stanislaw
Abstract: We discuss a branch of Ramsey theory concerning vertex Folkman numbers and how computer algorithms have been used to compute a new Folkman number. We write G ! (a1, . . . , ak)v if for every vertex k-coloring of an undirected simple graph G, a monochromatic Kai is forced in color i 2 {1, . . . , k}. The vertex Folkman number is defined as Fv(a1, . . . , ak; p) = min{|V (G)| : G ! (a1, . . . , ak)v ^ Kp 6 G}. Folkman showed in 1970 that this number exists for p > max{a1, . . . , ak}. Let m = 1+Pk i=1(ai−1) and a = max{a1, . . . , ak}, then Fv(a1, . . . , ak; p) = m for p > m, and Fv(a1, . . . , ak; p) = a +m for p = m. For p < m the situation is more difficult and much less is known. We show here that, for a case of p = m−1, Fv(2, 2, 3; 4) = 14.
Record URI: http://hdl.handle.net/1850/7993
Date: 2006

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