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- Title
On the 3-Color Ramsey Numbers R(C4,C4,Wn)
- Authors
Zhang, Xuemei; Chen, Yaojun; Cheng, T. C. Edwin
- Abstract
For given graphs G 1 , G 2 , ⋯ , G k , k ≥ 2 , the k-color Ramsey number, denoted by R (G 1 , G 2 , … , G k) , is the smallest integer N such that if we arbitrarily color the edges of a complete graph of order N with k colors, then it always contains a monochromatic copy of G i in color i, for some 1 ≤ i ≤ k . Let C m be a cycle of length m and W n a wheel of order n + 1 . In this paper, we show that R (C 4 , C 4 , W n) ≤ n + 4 n + 5 + 3 for n = 42 , 48 , 49 , 50 , 51 , 52 or n ≥ 56 . Furthermore, we prove that R (C 4 , C 4 , W ℓ 2 - ℓ) ≤ ℓ 2 + ℓ + 2 for ℓ ≥ 9 , and if ℓ is a prime power, then the equality holds.
- Publication
Graphs & Combinatorics, 2022, Vol 38, Issue 3, p1
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-022-02505-y