Computation of the Folkman number F e (3, 3; 5)

Abstract

With the help of computer algorithms, we improve the lower bound on the edge Folkman number Fe(3, 3; 5) and vertex Folkman number Fv(3, 3; 4), and, thus, show that the exact values of these numbers are 15 and 14, respectively. We also present computer enumeration of all critical graphs. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 41–49, 1999