Gyárfás et alâ. âdetermined the asymptotic value of the diagonalâ
âRamsey number of Cknâ, âR(Ckn,Ckn), generating the same result for k=3 due to Haxell et alâ. âRecentlyâ, âthe exact values of the Ramsey numbers of 3-uniform loose paths and cycles are completely determinedâ. âThese results are motivations to conjecture thatâ
âfor every n ≥ m ≥ 3 and k ≥ 3,â
â
R(Ckn,Ckm)=(k−1)n+⎣ |
m−1
2
|
⎦, |
|
â
âas mentioned by Omidi et alâ.
âMore recentlyâ, âit 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 oddâ. âHere we investigate this conjecture for k=5 and demonstrate that it holds for k=5 and sufficiently large nâ.
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