نتایج جستجو برای: ramsey number

تعداد نتایج: 1171359  

Journal: :Electr. J. Comb. 2012
András Gyárfás Ghaffar Raeisi

Asymptotic values of hypergraph Ramsey numbers for loose cycles (and paths) were determined recently. Here we determine some of them exactly, for example the 2-color hypergraph Ramsey number of a k-uniform loose 3-cycle or 4-cycle: R(Ck 3 , Ck 3 ) = 3k − 2 and R(Ck 4 , Ck 4 ) = 4k − 3 (for k > 3). For more than 3 colors we could prove only that R(C3 3 , C3 3 , C3 3) = 8. Nevertheless, the r-col...

2012
Kevin G. Milans Derrick Stolee Douglas B. West

We study an ordered version of hypergraph Ramsey numbers using linearly ordered vertex sets, due to Fox, Pach, Sudakov, and Suk. In the k-uniform ordered path, the edges are the sets of k consecutive vertices in a linear vertex order. Moshkovitz and Shapira described its ordered Ramsey number as the solution to an enumeration problem involving higher-order mulidimensional integer partitions. We...

Journal: :Discrete & Computational Geometry 2015
Josef Cibulka Pu Gao Marek Krcál Tomás Valla Pavel Valtr

We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by O(n3) and O(n10), in the convex and general case, respectively. We then apply similar methods to prove an nO(log(n)) upper bound on the Ramsey number of a path wit...

Journal: :Journal of Combinatorial Theory, Series B 2007

Journal: :Journal of Computer and Communications 2016

Journal: :The Electronic Journal of Combinatorics 2012

Journal: :The Journal of Combinatorics 2023

The size-Ramsey number $R^{(k)}(H)$ of a $k$-uniform hypergraph $H$ is the minimum edges in $G$ with property that each $2$-edge coloring contains monochromatic copy $H$. For $k\ge2$ and $n\in\mathbb{N}$, tight path on $n$ vertices $P^{(k)}_{n,k-1}$ defined as for which there an ordering its such edge set consists all $k$-element intervals consecutive this ordering. We show lower bound paths, i...

Journal: :Discussiones Mathematicae Graph Theory 2019

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