Skip to main content
Article thumbnail
Location of Repository

On the multi-colored Ramsey numbers of cycles

By Tomasz Łuczak, Miklós Simonovits and Jozef Skokan


For a graph L and an integer k≥2, Rk(L) denotes the smallest integer N for which for any edge-coloring of the complete graph KN by k colors there exists a color i for which the corresponding color class contains L as a subgraph. Bondy and Erdo″s conjectured that, for an odd cycle Cn on n vertices, Rk(Cn)=2 k-1(n-1)+1 for n>3. They proved the case when k = 2 and also provided an upper bound Rk(Cn)≤(k+ 2)!n. Recently, this conjecture has been verified for k = 3 if n is large. In this note, we prove that for every integer k≥4, Rk(Cn≤ k2kn+o «n» as n → ∞ When n is even, Sun Yongqi, Yang Yuansheng, Xu Feng, and Li Bingxi gave a construction, showing that Rk(C n≥(k-1)n-2k+ 4. Here we prove that if n is even, then R k(Cn≤kn+o(n) as n→∞

Topics: QA Mathematics
Publisher: Wiley-Blackwell
Year: 2011
DOI identifier: 10.1002/jgt.20572
OAI identifier:
Provided by: LSE Research Online
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.