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Paper   IPM / M / 16731
School of Mathematics
  Title:   Ramsey numbers of 5-uniform loose cycles
  Author(s):  Maryam Shahsiah
  Status:   To Appear
  Journal: Graphs Combin.
  Supported by:  IPM
  Abstract:
Gyárfás et al‎. ‎determined the asymptotic value of the diagonal‎ ‎Ramsey number of Ckn‎, ‎R(Ckn,Ckn), generating the same result for k=3 due to Haxell et al‎. ‎Recently‎, ‎the exact values of the Ramsey numbers of 3-uniform loose paths and cycles are completely determined‎. ‎These results are motivations to conjecture that‎ ‎for every nm ≥ 3 and k ≥ 3,‎ ‎
R(Ckn,Ckm)=(k−1)n+⎣ m−1

2
⎦,
‎ ‎as mentioned by Omidi et al‎. ‎More recently‎, ‎it is shown that this conjecture is true for n=m ≥ 2 and k ≥ 7 and for k=4 when n > m or n=m is odd‎. ‎Here we investigate this conjecture for k=5 and demonstrate that it holds for k=5 and sufficiently large n‎.


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