Ramsey problems for monotone paths in graphs and hypergraphs
Abstract
The study of ordered Ramsey numbers of monotone paths for graphs and hypergraphs has a long history, going back to the celebrated work by Erdos and Szekeres in the early days of Ramsey theory. In this paper we obtain several results in this area, establishing two conjectures of Mubayi and Suk and improving bounds due to Balko, Cibulka, Kr\'al and Kyncl. We also obtain a color-monotone version of the well-known Canonical Ramsey Theorem of Erdos and Rado, which could be of independent interest.
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