## Abstract

For bipartite graphs G _{1}, G _{2},..., G _{k}, the bipartite Ramsey number b(G _{1}, G _{2},..., G _{k}) is the least positive integer b so that any colouring of the edges of K _{b,b} with k colours will result in a copy of G _{i} in the ith colour for some i. A tree of diameter three is called a bistar, and will be denoted by B(s, t), where s ≥ 2 and t ≥ 2 are the degrees of the two support vertices. In this paper we will obtain some exact values for b(B(s, t), B(s, t)) and b(B(s, s), B(s, s)). Furtermore, we will show that if k colours are used, with k ≥ 2 and s ≥ 2, then (formula presented.). Finally, we show that for s ≥ 3 and k ≥ 2, the Ramsey number (formula presented.).

Original language | English |
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Pages (from-to) | 1175-1181 |

Number of pages | 7 |

Journal | Graphs and Combinatorics |

Volume | 30 |

Issue number | 5 |

DOIs | |

Publication status | Published - Sept 2014 |

## Keywords

- Bipartite graph
- Bistar
- Ramsey

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics