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Asymptotic bounds for irredundant and mixed Ramsey numbers

✍ Scribed by Guantao Chen; Johannes H. Hattingh; Cecil C. Rousseau

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
473 KB
Volume
17
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The irredundant Ramsey number s(m, n) is the smallest N such that in every red‐blue coloring of the edges of K~N~, either the blue graph contains an m‐element irredundant set or the red graph contains an n‐element irredundant set. The definition of the mixed Ramsey number t(m, n) differs from s(m, n) in that the n‐element irredundant set is replaced by an n‐element independent set. We prove asymptotic lower bounds for s(n, n) and t(m, n) (with m fixed and n large) and a general upper bound for t(3, n). Β© 1993 John Wiley & Sons, Inc.

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