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Paper
IPM / M / 16731 |
School of Mathematics
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Title: |
Ramsey numbers of 5-uniform loose cycles
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Author(s): |
Maryam Shahsiah
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Status: |
To Appear
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Journal: |
Graphs Combin.
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Supported by: |
IPM
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Abstract: |
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
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R(Ckn,Ckm)=(k−1)n+⎣ |
m−1
2
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⎦, |
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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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