# Ordered size Ramsey number of paths

@article{Balogh2018OrderedSR,
title={Ordered size Ramsey number of paths},
author={J{\'o}zsef Balogh and Felix Christian Clemen and Emily Heath and Mikhail Lavrov},
journal={Discret. Appl. Math.},
year={2018},
volume={276},
pages={13-18}
}
• Published 19 October 2018
• Mathematics
• Discret. Appl. Math.
5 Citations
• Mathematics
• 2020
The Erdős-Szekeres Theorem stated in terms of graphs says that any red-blue coloring of the edges of the ordered complete graph $K_{rs+1}$ contains a red copy of the monotone increasing path with $r$
• Chunlin You
• Mathematics
Acta Mathematicae Applicatae Sinica, English Series
• 2021
Let r ≥ 3 be an integer such that r − 2 is a prime power and let H be a connected graph on n vertices with average degree at least d and α ( H ) ≤ βn , where 0 < β < 1 is a constant. We prove that
• Chunlin You
• Mathematics
Acta Mathematicae Applicatae Sinica, English Series
• 2021
Let r ≥ 3 be an integer such that r − 2 is a prime power and let H be a connected graph on n vertices with average degree at least d and α(H) ≤ βn, where 0 < β < 1 is a constant. We prove that the
• Mathematics
Random Struct. Algorithms
• 2020
It is proved that for every edge-ordered graph $H$ on $n$ vertices, the authors have $r_{edge}(H;q) \leq 2^{c^qn^{2q-2}\log^q n}$, where $c$ is an absolute constant.

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This note provides another proof of this fact that actually gives a better bound, namely, $\^{r}$(Pn) < 137n for n sufficiently large.
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It is proved that, with high probability, any 2-edge-colouring of a random tournament on n vertices contains a monochromatic path of length Ω(n/ √ logn), which implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.
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Let denote the class of all graphsG which satisfyG→(G1,G2). As a way of measuring minimality for members of, we define thesize Ramsey number ř(G1,G2) by.We then investigate various questions