article published Josef Cibulka author Pu Gao author Marek Krcál author 33E21118-F248-11E8-B48F-1D18A9856A87 Tomáš Valla author Pavel Valtr author UlWa department HeEd department 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(n3) and O(n10), in the convex and general case, respectively. We then apply similar methods to prove an (Formula presented.) upper bound on the Ramsey number of a path with n ordered vertices. Springer2014 eng 1310.7004 00034677460000510.1007/s00454-014-9646-x 53164 - 79 Cibulka, J., Gao, P., Krcál, M., Valla, T., &#38; Valtr, P. (2014). On the geometric ramsey number of outerplanar graphs. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href="https://doi.org/10.1007/s00454-014-9646-x">https://doi.org/10.1007/s00454-014-9646-x</a> Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey number of outerplanar graphs. Discrete &#38; Computational Geometry. 53(1), 64–79. Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.” <i>Discrete &#38; Computational Geometry</i>, vol. 53, no. 1, Springer, 2014, pp. 64–79, doi:<a href="https://doi.org/10.1007/s00454-014-9646-x">10.1007/s00454-014-9646-x</a>. Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On the Geometric Ramsey Number of Outerplanar Graphs.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2014. <a href="https://doi.org/10.1007/s00454-014-9646-x">https://doi.org/10.1007/s00454-014-9646-x</a>. J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey number of outerplanar graphs,” <i>Discrete &#38; Computational Geometry</i>, vol. 53, no. 1. Springer, pp. 64–79, 2014. Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number of outerplanar graphs. <i>Discrete &#38; Computational Geometry</i>. 2014;53(1):64-79. doi:<a href="https://doi.org/10.1007/s00454-014-9646-x">10.1007/s00454-014-9646-x</a> J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete &#38; Computational Geometry 53 (2014) 64–79. 18422018-12-11T11:54:18Z2025-09-29T13:11:56Z