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Constrained Ramsey numbers for rainbow matching

✍ Scribed by Allan Siu Lun Lo

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 77 KB
Volume: 67
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20517

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✦ Synopsis

The Ramsey number R k (G) of a graph G is the minimum number N, such that any edge coloring of K N with k colors contains a monochromatic copy of G. The constrained Ramsey number f (G, T ) of the graphs G and T is the minimum number N, such that any edge coloring of K N with any number of colors contains a monochromatic copy of G or a rainbow copy of T . We show that these two quantities are closely related when T is a matching. Namely, for almost all graphs G, f (G, tK 2 ) = R t-1 (G) for t ≥ 2.

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