English

The Ramsey number of loose paths in 3-uniform hypergraphs

Combinatorics 2012-12-06 v3

Abstract

Recently, asymptotic values of 2-color Ramsey numbers for loose cycles and also loose paths were determined. Here we determine the 2-color Ramsey number of 3-uniform loose paths when one of the paths is significantly larger than the other: for every n5m4n\geq \Big\lfloor\frac{5m}{4}\Big\rfloor, we show that R(Pn3,Pm3)=2n+m+12.R(\mathcal{P}^3_n,\mathcal{P}^3_m)=2n+\Big\lfloor\frac{m+1}{2}\Big\rfloor.

Keywords

Cite

@article{arxiv.1209.4159,
  title  = {The Ramsey number of loose paths in 3-uniform hypergraphs},
  author = {Leila Maherani and Gholamreza Omidi and Ghaffar Raeisi and Maryam Shahsiah},
  journal= {arXiv preprint arXiv:1209.4159},
  year   = {2012}
}