### Abstract

Let G1 and G2 be two given graphs. The Ramsey number R(G1,G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or the complement of G contains a G2. A complete bipartite graph K1,n is called a star. The kipas of order n+1 is the graph obtained from a path of order n by adding a new vertex and joining it to all the vertices of the path. Alternatively, a kipas is a wheel with one edge on the rim deleted. Whereas for star-wheel Ramsey numbers not all exact values are known to date, in contrast we determine all exact values of star-kipas Ramsey numbers.

Original language | English |
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Pages (from-to) | 141-148 |

Number of pages | 8 |

Journal | Graphs and combinatorics |

Volume | 33 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2017 |

### Keywords

- EWI-27594
- MSC-05C
- Wheel
- IR-104073
- Kipas
- Star
- Ramsey number

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## Cite this

Li, B., Zhang, Y., & Broersma, H. (2017). An exact formula for all star-kipas Ramsey numbers.

*Graphs and combinatorics*,*33*(1), 141-148. https://doi.org/10.1007/s00373-016-1746-3