### Abstract

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.

Original language | Undefined |
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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

Zhang, Y., Broersma, H. J., & Chen, Y. (2015). Ramsey numbers of trees versus fans.

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