Diagonal Ramsey numbers of loose cycles in uniform hypergraphs

2015/03/03 by Omidi, Gholamreza, Shahsiah, Maryam
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.00937

Abstract

A k-uniform loose cycle C_n^k is a hypergraph with vertex set \v₁,v₂,…,v_n(k-1)\ and with the set of n edges e_i=\v_(i-1)(k-1)+1,v_(i-1)(k-1)+2,…,v_(i-1)(k-1)+k\, 1≤ i≤ n, where we use mod n(k-1) arithmetic. The Ramsey number R(C^k_n,C^k_n) is asymptotically (1)/(2)(2k-1)n as has been proved by Gyárfás, Sárközy and Szemerédi. In this paper, we investigate to determining the exact value of diagonal Ramsey number of C^k_n and we show that for n≥ 2 and k≥ 8 R(C^k_n,C^k_n)=(k-1)n+\lfloor(n-1)/(2)\rfloor.

Related

• Ramsey numbers of uniform loose paths and cycles
• Ramsey numbers of 4-uniform loose cycles
• Ramsey numbers of 5-uniform loose cycles
• Ramsey numbers of 3-uniform loose paths and loose cycles
• The Ramsey number of loose paths in 3-uniform hypergraphs