The planar Ramsey number.

Abstract: For two given graphs and , the planar Ramsey number is the smallest integer such that for any planar graph on vertices, either contains or its complement contains . Let denote a cycle of length and a complete graph of order . Sun, Yang, Lin and Song conjectured that and the conjecture was proved for . In this paper, it is shown that which confirms the conjecture for . [Copyright &y& Elsevier]