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Bounds for two multicolor Ramsey numbers concerning quadrilaterals.
- Source :
-
Finite Fields & Their Applications . Mar2022, Vol. 79, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- For k given graphs H 1 , ... , H k , k ≥ 2 , the k -color Ramsey number, denoted by R (H 1 , ... , H 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 H i colored with i , for some 1 ≤ i ≤ k. Let C m be a cycle of length m , K 1 , n a star of order n + 1 and W n a wheel of order n + 1. In this paper, by using algebraic and probabilistic methods, we first give two lower bounds for (k + 1) -color Ramsey number R (C 4 , ... , C 4 , K 1 , n) for some special n , which shows the upper bound due to Zhang et al. (2019) is tight in some sense, and then establish a general lower bound for R (C 4 , ... , C 4 , K 1 , n) in terms of n and k , which extends the classical result of Burr et al. (1989). Moreover, we show that R (C 4 , ... , C 4 , K 1 , n) = R (C 4 , ... , C 4 , W n) for sufficiently large n. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RAMSEY numbers
*QUADRILATERALS
*COMPLETE graphs
*FINITE fields
*RANDOM graphs
Subjects
Details
- Language :
- English
- ISSN :
- 10715797
- Volume :
- 79
- Database :
- Academic Search Index
- Journal :
- Finite Fields & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 155259873
- Full Text :
- https://doi.org/10.1016/j.ffa.2022.101999