### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 994-999 |

Number of pages | 6 |

Journal | Discrete mathematics |

Volume | 338 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 2015 |

### Keywords

- Tree
- Star
- Fan
- Ramsey number

### Cite this

*Discrete mathematics*,

*338*(6), 994-999. https://doi.org/10.1016/j.disc.2015.01.030

}

*Discrete mathematics*, vol. 338, no. 6, pp. 994-999. https://doi.org/10.1016/j.disc.2015.01.030

**Ramsey numbers of trees versus fans.** / Zhang, Yanbo; Broersma, Haitze J.; Chen, Yaojun.

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

TY - JOUR

T1 - Ramsey numbers of trees versus fans

AU - Zhang, Yanbo

AU - Broersma, Haitze J.

AU - Chen, Yaojun

PY - 2015/6

Y1 - 2015/6

N2 - For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integerN such that, for any graph G of order N, either G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. Let Tn be a tree of order n, Sn a star of order n, and Fm a fan of order 2m + 1, i.e., m triangles sharing exactly one vertex. In this paper, we prove that R(Tn, Fm) = 2n − 1 for n ≥ 3m^2 − 2m − 1, and if Tn = Sn, then the range can be replaced by n ≥ max{m(m − 1) + 1, 6(m − 1)}, which is tight in some sense.

AB - For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integerN such that, for any graph G of order N, either G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. Let Tn be a tree of order n, Sn a star of order n, and Fm a fan of order 2m + 1, i.e., m triangles sharing exactly one vertex. In this paper, we prove that R(Tn, Fm) = 2n − 1 for n ≥ 3m^2 − 2m − 1, and if Tn = Sn, then the range can be replaced by n ≥ max{m(m − 1) + 1, 6(m − 1)}, which is tight in some sense.

KW - Tree

KW - Star

KW - Fan

KW - Ramsey number

U2 - 10.1016/j.disc.2015.01.030

DO - 10.1016/j.disc.2015.01.030

M3 - Article

VL - 338

SP - 994

EP - 999

JO - Discrete mathematics

JF - Discrete mathematics

SN - 0012-365X

IS - 6

ER -