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Planar Ramsey Numbers

✍ Scribed by R. Steinberg; C.A. Tovey

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 240 KB
Volume: 59
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1993.1070

No coin nor oath required. For personal study only.

✦ Synopsis

The planar Ramsey number (P R(k, l)(k, l \geqslant 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 (P R(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 (\lfloor n / 3\rfloor+1 . \quad 1993) Academic Press. Inc.

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