3-均匀紧路径的大小Ramsey数

Q2 Mathematics

Advances in Combinatorics Pub Date : 2019-07-18 DOI:10.19086/aic.24581

Jie Han, Y. Kohayakawa, Shoham Letzter, G. Mota, Olaf Parczyk

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引用次数: 7

摘要

给定超图H，Ramsey数r（H）是最小整数m，使得存在一个具有m条边的图G，其性质是在具有两种颜色的G的边的任何着色中都存在H的单色副本。我们证明了n个顶点P_n上的3-均匀紧路径的Ramsey数在n中是线性的，即r（P_n）=O（n）。这回答了Dudek、Fleur、Mubayi和Rödl关于3-一致超图的一个问题[关于超图的大小Ramsey数，J.Graph Theory 86（2016），417-434]，他证明了R（P_n）=O（n^1.5*log^1.5n）。

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The size-Ramsey number of 3-uniform tight paths

Given a hypergraph H, the size-Ramsey number r(H) is the smallest integer m such that there exists a graph G with m edges with the property that in any colouring of the edges of G with two colours there is amonochromatic copy of H. We prove that the size-Ramsey number of the 3-uniform tight path on n vertices P_n is linear in n, i.e., r(P_n)=O(n). This answers a question by Dudek, Fleur, Mubayi, and Rödl for 3-uniform hypergraphs [On the size-Ramsey number of hypergraphs, J. Graph Theory 86 (2016), 417-434], who proved r(P_n)=O(n^1.5*log^1.5 n).

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来源期刊

Advances in Combinatorics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

3.10

自引率

0.00%

发文量