On the Geometric Ramsey Number of Outerplanar Graphs

Abstract

We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth- outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on vertices are bounded by and , in the convex and general case, respectively.

We then apply similar methods to prove an upper bound on the Ramsey number of a path with ordered vertices.

Keywords

• Geometric Ramsey theory
• Outerplanar graph
• Ordered Ramsey theory
• Pathwidth