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Planar Ramsey numbers

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

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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:
Additional Information: © 1993 Elsevier B.V.
Divisions: Management
Subjects: Q Science > QA Mathematics
Date Deposited: 16 Apr 2009 09:30
Last Modified: 15 May 2024 23:33

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