The Ramsey numbers R(Tn, W6) for Δ(Tn) ≥ n−3

✍ Scribed by Yaojun Chen; Yunqing Zhang; Kemin Zhang

• Book ID: 104349696
• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 304 KB
• Volume: 17
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(04)90064-x

✦ Synopsis

Let T~ denote a tree of order n and Wm a wheel of order m + 1. In a previous paper, we evaluated the Ramsey number R(Tn, W,~) in the cases where Tn is the star of order n and m = 6 or m is odd and n > m-1 > 2. In this paper, we determine R(Tn, W6) in the case where the maximum degree of T~ is at least n -3. Our results show that a recent conjecture of Baskoro et al. is false. (~) 2004 Elsevier Ltd. All rights reserved. Keywords--Ramsey number, Tree, Wheel.

of every length l, 3 < 1 < n.

Many thanks to the anonymous referees for their many helpful comments and suggestions, especially the simple proof of Theorem 1, which have considerably improved the presentation of the paper.