Steinberg, Richard 
ORCID: 0000-0001-9636-472X 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 |
|---|---|
| Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |
| Additional Information: | © 1993 Elsevier B.V. |
| Divisions: | Management |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 16 Apr 2009 09:30 |
| Last Modified: | 13 Sep 2024 21:00 |
| URI: | http://eprints.lse.ac.uk/id/eprint/23593 |
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