Steinberg, Richard and Tovey, Craig A.
(1993)
*Planar Ramsey numbers.*
Journal of Combinatorial Theory, Series B, 59 (2).
pp. 288-296.
ISSN 0095-8956

## Abstract

The planar Ramsey number PR(k, l) (k, l ≥ 2) is the smallest integer n such that any planar graph on n vertices contains either a complete graph on k vertices or an independent set of size l. We find exact values of PR(k, l) for all k and l. Included is a proof of a 1976 conjecture due to Albertson, Bollobás, and Tucker that every triangle-free planar graph on n vertices contains an independent set of size left floorn/3right floor + 1.

Item Type: | Article |
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Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |

Additional Information: | © 1993 Elsevier B.V. |

Subjects: | Q Science > QA Mathematics |

Sets: | Research centres and groups > Management Science Group Departments > Management |

Date Deposited: | 16 Apr 2009 09:30 |

Last Modified: | 28 Feb 2018 16:34 |

URI: | http://eprints.lse.ac.uk/id/eprint/23593 |

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