### Abstract

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

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 6 |

Publication status | Published - 2002 |

### Publication series

Name | Memorandum |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1634 |

ISSN (Print) | 0169-2690 |

### Fingerprint

### Keywords

- MSC-05C55
- IR-65821
- EWI-3454
- MSC-05D10
- METIS-208268

### Cite this

*The Ramsey numbers of large cycles versus small wheels*. (Memorandum; No. 1634). Enschede: University of Twente, Department of Applied Mathematics.

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*The Ramsey numbers of large cycles versus small wheels*. Memorandum, no. 1634, University of Twente, Department of Applied Mathematics, Enschede.

**The Ramsey numbers of large cycles versus small wheels.** / Surahmat; Baskoro, E.T.; Broersma, H.J.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - The Ramsey numbers of large cycles versus small wheels

AU - Surahmat, null

AU - Baskoro, E.T.

AU - Broersma, H.J.

N1 - Imported from MEMORANDA

PY - 2002

Y1 - 2002

N2 - For two given graphs $G$ and $H$, the \textit{Ramsey number} $R(G,H)$ is the smallest positive integer $N$ such that for every graph $F$ of order $N$ the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we determine the Ramsey number $R(C_n,W_{m})$ for $m=4$ and $m=5$. We show that $R(C_{n},W_{4})=2n-1$ and $R(C_n,W_5)=3n-2$ for $n\geq 5$. For larger wheels it remains an open problem to determine $R(C_n,W_{m})$.

AB - For two given graphs $G$ and $H$, the \textit{Ramsey number} $R(G,H)$ is the smallest positive integer $N$ such that for every graph $F$ of order $N$ the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we determine the Ramsey number $R(C_n,W_{m})$ for $m=4$ and $m=5$. We show that $R(C_{n},W_{4})=2n-1$ and $R(C_n,W_5)=3n-2$ for $n\geq 5$. For larger wheels it remains an open problem to determine $R(C_n,W_{m})$.

KW - MSC-05C55

KW - IR-65821

KW - EWI-3454

KW - MSC-05D10

KW - METIS-208268

M3 - Report

T3 - Memorandum

BT - The Ramsey numbers of large cycles versus small wheels

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -