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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 14713
   School of Mathematics
  Title: Diagonal Ramsey numbers of loose cycles in uniform hypergraphs
  Author(s):
1 . G.R. Omidi
2 . M. Shahsiah
  Status: Published
  Journal: SIAM J. Discrete Math.
  Vol.: 31
  Year: 2017
  Pages: 1634-1669
  Supported by: IPM
  Abstract:
A k-uniform loose cycle Cnk is a hypergraph with vertex set {v1,v2,…,vn(k−1)} and the set of n edges ei={v(i−1)(k−1)+1,v(i−1)(k−1)+2,…, v(i−1)(k−1)+k}, 1 ≤ in, where we use mod n(k−1) arithmetic. The diagonal Ramsey number of Ckn, R(Ckn,Ckn), is asymptotically [1/2](2k−1)n, as has been proved by Gyárfás, Sárközy, and Szemerédi [Electron. J. Combin., 15 (2008), #R126]. In this paper, we investigate to determine the exact value of R(Ckn,Ckn) and we show that for n ≥ 2 and k ≥ 8, R(Ckn,Ckn)=(k−1)n+⎣[(n−1)/2]⎦.


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