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arXiv · 1310.7004

On the Geometric Ramsey Number of Outerplanar Graphs

Josef Cibulka·Pu Gao·Marek Krčál·Tomáš Valla·Pavel Valtr
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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.

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Josef Cibulka, Pu Gao, Marek Krčál, Tomáš Valla, Pavel Valtr. 2013-11-13. On the Geometric Ramsey Number of Outerplanar Graphs. https://doi.org/10.1007/s00454-014-9646-x

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