The Ramsey number of a long even cycle versus a star

Peter Allen; Tomasz Łuczak; Joanna Polcyn; Yanbo Zhang

The Ramsey number of a long even cycle versus a star

Combinatorics 2020-10-21 v2

Authors: Peter Allen , Tomasz Łuczak , Joanna Polcyn , Yanbo Zhang

Abstract

We find the exact value of the Ramsey number $R(C_{2\ell},K_{1,n})$ , when $\ell$ and $n=O(\ell^{10/9})$ are large. Our result is closely related to the behaviour of Tur\'an number $ex(N, C_{2\ell})$ for an even cycle whose length grows quickly with $N$ .

Keywords

ramsey number even cycle star graph turán number extremal graph theory

Cite

@article{arxiv.2003.03310,
  title  = {The Ramsey number of a long even cycle versus a star},
  author = {Peter Allen and Tomasz Łuczak and Joanna Polcyn and Yanbo Zhang},
  journal= {arXiv preprint arXiv:2003.03310},
  year   = {2020}
}

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