### Abstract

Original language | English |
---|---|

Pages (from-to) | 2284-2287 |

Number of pages | 7 |

Journal | Discrete mathematics |

Volume | 339 |

Issue number | 9 |

Early online date | 6 May 2016 |

DOIs | |

Publication status | Published - 6 Sep 2016 |

### Fingerprint

### Keywords

- Fan
- Tree
- Ramsey number
- Wheel

### Cite this

*Discrete mathematics*,

*339*(9), 2284-2287. https://doi.org/10.1016/j.disc.2016.03.013

}

*Discrete mathematics*, vol. 339, no. 9, pp. 2284-2287. https://doi.org/10.1016/j.disc.2016.03.013

**On fan-wheel and tree-wheel Ramsey numbers.** / Zhang, Yanbo; Zhang, Yanbo; Broersma, Haitze J.; Chen, Yaojun.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - On fan-wheel and tree-wheel Ramsey numbers

AU - Zhang, Yanbo

AU - Zhang, Yanbo

AU - Broersma, Haitze J.

AU - Chen, Yaojun

PY - 2016/9/6

Y1 - 2016/9/6

N2 - For graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. Let Tn denote a tree of order n, Wn a wheel of order n+1 and Fn a fan of order 2n+1. We establish Ramsey numbers for fans and trees versus wheels of even order, thereby extending several known results. In particular, we prove that R(Fn,Wm)=6n+1 for odd m≥3 and n≥(5m+3)/4, and that R(Tn,Wm)=3n−2 for odd m≥3 and n≥m−2, and Tn being a tree for which the Erdős–Sós Conjecture holds.

AB - For graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. Let Tn denote a tree of order n, Wn a wheel of order n+1 and Fn a fan of order 2n+1. We establish Ramsey numbers for fans and trees versus wheels of even order, thereby extending several known results. In particular, we prove that R(Fn,Wm)=6n+1 for odd m≥3 and n≥(5m+3)/4, and that R(Tn,Wm)=3n−2 for odd m≥3 and n≥m−2, and Tn being a tree for which the Erdős–Sós Conjecture holds.

KW - Fan

KW - Tree

KW - Ramsey number

KW - Wheel

U2 - 10.1016/j.disc.2016.03.013

DO - 10.1016/j.disc.2016.03.013

M3 - Article

VL - 339

SP - 2284

EP - 2287

JO - Discrete mathematics

JF - Discrete mathematics

SN - 0012-365X

IS - 9

ER -