1Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary 2University of South Carolina, Columbia, USA 3Universidad de Costa Rica, San José, Costa Rica and Central European University, Budapest, Hungary
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 1035-1042
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Nika Salia; Casey Tompkins; Zhiyu Wang; Oscar Alonso Zamora Luna; Nika Salia; Casey Tompkins; Zhiyu Wang; Oscar Alonso Zamora Luna. Ramsey numbers of Berge-hypergraphs and related structures. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 1035-1042. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a105/
@article{AMUC_2019_88_3_a105,
author = {Nika Salia and Casey Tompkins and Zhiyu Wang and Oscar Alonso Zamora Luna and Nika Salia and Casey Tompkins and Zhiyu Wang and Oscar Alonso Zamora Luna},
title = { Ramsey numbers of {Berge-hypergraphs} and related structures},
journal = {Acta mathematica Universitatis Comenianae},
pages = {1035--1042},
year = {2019},
volume = {88},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a105/}
}
TY - JOUR
AU - Nika Salia
AU - Casey Tompkins
AU - Zhiyu Wang
AU - Oscar Alonso Zamora Luna
AU - Nika Salia
AU - Casey Tompkins
AU - Zhiyu Wang
AU - Oscar Alonso Zamora Luna
TI - Ramsey numbers of Berge-hypergraphs and related structures
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 1035
EP - 1042
VL - 88
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a105/
ID - AMUC_2019_88_3_a105
ER -
%0 Journal Article
%A Nika Salia
%A Casey Tompkins
%A Zhiyu Wang
%A Oscar Alonso Zamora Luna
%A Nika Salia
%A Casey Tompkins
%A Zhiyu Wang
%A Oscar Alonso Zamora Luna
%T Ramsey numbers of Berge-hypergraphs and related structures
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 1035-1042
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a105/
%F AMUC_2019_88_3_a105
For a graph $G=(V,E)$, a hypergraph $\cH$ is called a \textit{Berge}-$G$, denoted by $BG$, if there exists an injection $f: E(G) \to E(\cH)$ such that for every $e \in E(G)$, $e \subseteq f(e)$. Let the Ramsey number $R^r(BG,BG)$ be the smallest integer $n$ such that for any $2$-edge-coloring of a complete $r$-uniform hypergraph on $n$ vertices, there is a monochromatic Berge-$G$ subhypergraph.In this paper, we show that the 2-color Ramsey number of Berge cliques is linear. In particular, we show that $R^3(BK_s, BK_t) = s+t-3$ for $s,t \geq 4$ and $\max(s,t) \geq 5$ where $BK_n$ is a Berge-$K_n$ hypergraph. We also investigate the Ramsey number of tracehypergraphs, suspension hypergraphs and expansion hypergraphs.
