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On the 3-Color Ramsey Numbers R(C4,C4,Wn)
- Source :
-
Graphs & Combinatorics . Jun2022, Vol. 38 Issue 3, p1-9. 9p. - Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09110119
- Volume :
- 38
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Graphs & Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 157160110
- Full Text :
- https://doi.org/10.1007/s00373-022-02505-y