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On three color Ramsey numbers [formula omitted].
- Source :
-
Discrete Mathematics . Feb2019, Vol. 342 Issue 2, p285-291. 7p. - Publication Year :
- 2019
-
Abstract
- Abstract For k 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 colored with i , for some 1 ≤ i ≤ k. Let C m be a cycle of length m and K 1 , n a star of order n + 1. In this paper, firstly we give a general upper bound of R (C 4 , C 4 , ... , C 4 , K 1 , n). In particular, for the 3-color case, we have R (C 4 , C 4 , K 1 , n) ≤ n + 4 n + 5 + 3 and this bound is tight in some sense. Furthermore, we prove that R (C 4 , C 4 , K 1 , n) ≤ n + 4 n + 5 + 2 for all n = ℓ 2 − ℓ and ℓ ≥ 2 , and if ℓ is a prime power, then the equality holds. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 342
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 133187531
- Full Text :
- https://doi.org/10.1016/j.disc.2018.09.030