The 3-colored Ramsey number of odd cycles
Kohayakawa, Y., Simonovits, M. & Skokan, J.
(2005).
The 3-colored Ramsey number of odd cycles.
Electronic Notes in Discrete Mathematics,
19(1), 397-402.
https://doi.org/10.1016/j.endm.2005.05.053
(2005).
The 3-colored Ramsey number of odd cycles.
Electronic Notes in Discrete Mathematics,
19(1), 397-402.
https://doi.org/10.1016/j.endm.2005.05.053
For graphs L1, . . . ,Lk, the Ramsey number R(L1, . . . ,Lk) is the minimum integer N satisfying that for any coloring of the edges of the complete graph KN on N vertices by k colors there exists a color i for which the corresponding color class contains Li as a subgraph. In 1973, Bondy and Erd˝os conjectured that if n is odd and Cn denotes the cy- cle on n vertices, then R(Cn,Cn,Cn) = 4n − 3. In 1999, Luczak proved that R(Cn,Cn,Cn) = 4n + o(n), where o(n)/n ! 0 as n ! 1. In this paper we strengthen Luczak’s result and verify this conjecture for n sufficiently large.