Upper bounds for Ramsey numbers Original Research Article

The Ramsey number R(G1,G2,…,Gk) is the least integer p so that for any k-edge coloring of the complete graph Kp, there is a monochromatic copy of Gi of color i. In this paper, we derive upper bounds of R(G1,G2,…,Gk) for certain graphs Gi. In particular, these bounds show that R(9,9)⩽6588 and R(10,10)⩽23556 improving the previous best bounds of 6625 and 23854.