Planar Ramsey Numbers of Four Cycles Versus Wheels

Chen Yaojun; Miao Zhengke; Zhou Guofei

Planar Ramsey Numbers of Four Cycles Versus Wheels

Combinatorics 2013-04-25 v1

Authors: Chen Yaojun , Miao Zhengke , Zhou Guofei

Abstract

For two given graphs $G$ and $H$ the planar Ramsey number $PR(G,H)$ is the smallest integer $n$ such that every planar graph $F$ on $n$ vertices either contains a copy of $G$ , or its complement contains a copy of $H$ . In this paper, we first characterize some structural properties of $C_4$ -free planar graphs, and then we determine all planar Ramsey numbers $PR(C_4, W_n)$ , for $n\ge 3$ .

Keywords

planar Ramsey numbers four cycles wheels planar graphs graph complement structural properties extremal graph theory

Cite

@article{arxiv.1304.6466,
  title  = {Planar Ramsey Numbers of Four Cycles Versus Wheels},
  author = {Chen Yaojun and Miao Zhengke and Zhou Guofei},
  journal= {arXiv preprint arXiv:1304.6466},
  year   = {2013}
}

Planar Ramsey Numbers of Four Cycles Versus Wheels

Abstract

Keywords

Cite

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