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Threshold functions for asymmetric Ramsey properties with respect to vertex colorings

✍ Scribed by Bernd Kreuter

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 668 KB
Volume: 9
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199610)9:3<335::aid-rsa5>3.0.co;2-y

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✦ Synopsis

In this note we investigate Ramsey properties of random graphs. The threshold functions for symmetric Ramsey properties with respect to vertex colorings were determined by tuczak, Rucinski, and Voigt . As a generalization of this problem we consider asymmetric Ramsey properties and establish the values of the threshold functions. Furthermore, we investigate canonical colorings.

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We consider the binomial random graph G and determine a sharp threshold p function for the edge-Ramsey property G ª C l 1 , . . . , C l r Ž . p for all l , . . . , l , where C l denotes the cycle of length l. As deterministic consequences of 1 r our results, we prove the existence of sparse graphs