### Abstract

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

Pages (from-to) | 110-114 |

Number of pages | 5 |

Journal | Electronic journal of graph theory and applications |

Volume | 2 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 |

### Keywords

- EWI-25792
- MSC-04C
- Quadrilateral
- Ramsey number
- IR-94683
- 4-Cycle
- Wheel
- METIS-309924
- Star

### Cite this

*Electronic journal of graph theory and applications*,

*2*(2), 110-114. https://doi.org/10.5614/ejgta.2014.2.2.3

}

*Electronic journal of graph theory and applications*, vol. 2, no. 2, pp. 110-114. https://doi.org/10.5614/ejgta.2014.2.2.3

**A remark on star-C4 and wheel-C4 Ramsey numbers.** / Zhang, Yanbo; Broersma, Haitze J.; Chen, Yaojun.

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

TY - JOUR

T1 - A remark on star-C4 and wheel-C4 Ramsey numbers

AU - Zhang, Yanbo

AU - Broersma, Haitze J.

AU - Chen, Yaojun

N1 - eemcs-eprint-25792 http://eprints.ewi.utwente.nl/25792

PY - 2014

Y1 - 2014

N2 - Given two graphs G1 and G2, the Ramsey number R(G1;G2) is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Cn denote a cycle of order n, Wn a wheel of order n+1 and Sn a star of order n. In this paper, it is shown that R(Wn;C4) = R(Sn+1;C4) for n ≥ 6. Based on this result and Parsons' results on R(Sn+1;C4), we establish the best possible general upper bound for R(Wn;C4) and determine some exact values for R(Wn;C4).

AB - Given two graphs G1 and G2, the Ramsey number R(G1;G2) is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Cn denote a cycle of order n, Wn a wheel of order n+1 and Sn a star of order n. In this paper, it is shown that R(Wn;C4) = R(Sn+1;C4) for n ≥ 6. Based on this result and Parsons' results on R(Sn+1;C4), we establish the best possible general upper bound for R(Wn;C4) and determine some exact values for R(Wn;C4).

KW - EWI-25792

KW - MSC-04C

KW - Quadrilateral

KW - Ramsey number

KW - IR-94683

KW - 4-Cycle

KW - Wheel

KW - METIS-309924

KW - Star

U2 - 10.5614/ejgta.2014.2.2.3

DO - 10.5614/ejgta.2014.2.2.3

M3 - Article

VL - 2

SP - 110

EP - 114

JO - Electronic journal of graph theory and applications

JF - Electronic journal of graph theory and applications

SN - 2338-2287

IS - 2

ER -