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- W2962912234 abstract "An ordered graph is a simple graph with an ordering on its vertices. Define the ordered path Pn to be the monotone increasing path with n edges. The ordered size Ramsey number r̃(Pr,Ps) is the minimum number m for which there exists an ordered graph H with m edges such that every two-coloring of the edges of H contains a red copy of Pr or a blue copy of Ps. For 2≤r≤s, we show 18r2s≤r̃(Pr,Ps)≤Cr2s(logs)3, where C>0 is an absolute constant. This problem is motivated by the recent results of Bucić et al. (2019) and Letzter and Sudakov (2019) for oriented graphs." @default.
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- W2962912234 date "2020-04-01" @default.
- W2962912234 modified "2023-09-23" @default.
- W2962912234 title "Ordered size Ramsey number of paths" @default.
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- W2962912234 doi "https://doi.org/10.1016/j.dam.2019.02.002" @default.
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