### Abstract

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

Pages (from-to) | 3.21 |

Number of pages | 8 |

Journal | Electronic journal of combinatorics |

Volume | 22 |

Issue number | 3 |

State | Published - 14 Aug 2015 |

### Keywords

- MSC-05C
- EWI-26317
- Ramsey number
- IR-98275
- Path
- METIS-314968
- Kipas

### Cite this

*Electronic journal of combinatorics*,

*22*(3), 3.21.

}

*Electronic journal of combinatorics*, vol 22, no. 3, pp. 3.21.

**Closing the gap on path-kipas Ramsey numbers.** / Li, Binlong; Zhang, Yanbo; Bielak, Halina; Broersma, Haitze J.; Holub, Premysl.

Research output: Scientific - peer-review › Article

TY - JOUR

T1 - Closing the gap on path-kipas Ramsey numbers

AU - Li,Binlong

AU - Zhang,Yanbo

AU - Bielak,Halina

AU - Broersma,Haitze J.

AU - Holub,Premysl

N1 - eemcs-eprint-26317

PY - 2015/8/14

Y1 - 2015/8/14

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 Pn denote a path of order n and K^m a kipas of order m + 1, i.e., the graph obtained from a Pm by adding one new vertex v and edges from v to all vertices of the Pm. We close the gap in existing knowledge on exact values of the Ramsey numbers R(Pn,K^m) by determining the exact values for the remaining open cases.

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 Pn denote a path of order n and K^m a kipas of order m + 1, i.e., the graph obtained from a Pm by adding one new vertex v and edges from v to all vertices of the Pm. We close the gap in existing knowledge on exact values of the Ramsey numbers R(Pn,K^m) by determining the exact values for the remaining open cases.

KW - MSC-05C

KW - EWI-26317

KW - Ramsey number

KW - IR-98275

KW - Path

KW - METIS-314968

KW - Kipas

M3 - Article

VL - 22

SP - 3.21

JO - Electronic journal of combinatorics

T2 - Electronic journal of combinatorics

JF - Electronic journal of combinatorics

SN - 1077-8926

IS - 3

ER -