Bibliographic Details
| Title: |
LARGE BOOK-CYCLE RAMSEY NUMBERS. |
| Authors: |
QIZHONG LIN, XING PENG |
| Superior Title: |
SIAM Journal on Discrete Mathematics; 2021, Vol. 35 Issue 1, p532-545, 14p |
| Subject Terms: |
RAMSEY numbers, MATHEMATICS |
| People: |
ROUSSEAU, Jean-Jacques, 1712-1778 |
| Abstract: |
Let B(k) n be the book graph which consists of n copies of Kk+1 all sharing a common Kk, and let Cm be a cycle of length m. In this paper, we first determine the exact value of r(B(2) n,Cm) for 8 9n + 112 leq m leq lceil 3n 2 rceil + 1 and n geq 1000. This answers a question of Faudree, Rousseau, and Sheehan [Ars Combin., 31 (1991), pp. 239--248] in a stronger form when m and n are large. Building upon this exact result, we are able to determine the asymptotic value of r(B(k) n,Cn) for each k geq 3. Namely, we prove that for each k geq 3, r(B(k) n ,Cn) = (k + 1 + ok(1))n. This extends a result due to Rousseau and Sheehan [J. London Math. Soc., 18 (1978), pp. 392--396]. [ABSTRACT FROM AUTHOR] |
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| Database: |
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