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Paper   IPM / M / 14713
School of Mathematics
  Title:   Diagonal Ramsey numbers of loose cycles in uniform hypergraphs
1.  G.R. Omidi
2.  M. Shahsiah
  Status:   Published
  Journal: SIAM J. Discrete Math.
  Vol.:  31
  Year:  2017
  Pages:   1634-1669
  Supported by:  IPM
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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