The edge Folkman number F_e(3,3; 4) is greater than 19

摘要

We improve the known lower bound of 19 on the edge Folkman number (3,3;4) by proving with the help of a computer that F_e(3,3;4) > 20. We also obtain the new bounds 20 ≤ F_v(2,3,3;4) ≤≤ 24 on the vertex Folkman number F_v(2.3.3;4).