Abstract
We 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 also prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases.
This research was started at the 2nd Emléktabla Workshop held in Gyöngyöstarján, January 24–27, 2011. Research was supported by the project CE-ITI (GAČR P202/12/G061) of the Czech Science Foundation and by the grant SVV-2012-265313 (Discrete Methods and Algorithms). Josef Cibulka and Pavel Valtr were also supported by the project no. 52410 of the Grant Agency of Charles University. Pu Gao was supported by the Humboldt Foundation and is currently affiliated with University of Toronto.
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© 2013 Scuola Normale Superiore Pisa
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Cibulka, J., Gao, P., Krčál, M., Valla, T., Valtr, P. (2013). Polynomial bounds on geometric Ramsey numbers of ladder graphs. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_28
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DOI: https://doi.org/10.1007/978-88-7642-475-5_28
Publisher Name: Edizioni della Normale, Pisa
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