| Autor: |
Geneson, Jesse, Holmes, Amber, Liu, Xujun, Neidinger, Dana, Pehova, Yanitsa, Wass, Isaac |
| Rok vydání: |
2019 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
An ordered graph $\mathcal{G}$ is a simple graph together with a total ordering on its vertices. The (2-color) Ramsey number of $\mathcal{G}$ is the smallest integer $N$ such that every 2-coloring of the edges of the complete ordered graph on $N$ vertices has a monochromatic copy of $\mathcal{G}$ that respects the ordering. In this paper we investigate the effect of various graph operations on the Ramsey number of a given ordered graph, and detail a general framework for applying results on extremal functions of 0-1 matrices to ordered Ramsey problems. We apply this method to give upper bounds on the Ramsey number of ordered matchings arising from sum-decomposable permutations, an alternating ordering of the cycle, and an alternating ordering of the tight hyperpath. We also construct ordered matchings on $n$ vertices whose Ramsey number is $n^{q+o(1)}$ for any given exponent $q\in(1,2)$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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