Complete Graph-Tree Planar Ramsey Numbers.

For two given graphs G 1 and G 2 , the planar Ramsey number P R (G 1 , G 2) is the smallest integer N such that every planar graph G on N vertices either contains a copy of G 1 or its complement contains a copy of G 2 . In this paper, we determine all planar Ramsey numbers for the complete graphs versus trees. [ABSTRACT FROM AUTHOR]