Ramsey Numbers of 5-Uniform Loose Cycles

Abstract

Gyárfás et al. determined the asymptotic value of the diagonal Ramsey number of Cnk, R(Cnk,Cnk), 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 n≥ m≥ 3 and k≥ 3 , R(Cnk,Cmk)=(k-1)n+⌊m-12⌋,as mentioned by Omidi et al. More recently, it has been 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. © 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.