On the Geometric Ramsey Number of Outerplanar Graphs

Abstract

We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on $2n$ vertices are bounded by $O(n^3)$ and $O(n^{10})$, in the convex and general case, respectively. We then apply similar methods to prove an $n^{O(\log (n))}$ upper bound on the Ramsey number of a path with $n$ ordered vertices.

15 pages, 7 figures

References in corpus (1)

• Erdos-Szekeres-type theorems for monotone paths and convex bodies