Taiwanese Journal of Mathematics


Yusheng Li

Full-text: Open access


We sketch the ideas in the proofs of results on Ramsey numbers of a cycle, particularly in many colors, in which one is due to professor Ko-Wei Lih and the author for the right order of magnitude of Ramsey number $r_k(C_{2m})$ as $k\to\infty$ for $m=2,3,5$.

Article information

Taiwanese J. Math., Volume 12, Number 4 (2008), 1007-1013.

First available in Project Euclid: 18 July 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C55: Generalized Ramsey theory [See also 05D10]

Ramsey number algebraic construction probabilistic method bound


Li, Yusheng. RAMSEY NUMBERS OF A CYCLE. Taiwanese J. Math. 12 (2008), no. 4, 1007--1013. doi:10.11650/twjm/1500404994. https://projecteuclid.org/euclid.twjm/1500404994

Export citation


  • H. Abbott and D. Hanson, A problem of Schur and its generalizations, Acta Arith., 20 (1972), 175-187.
  • B. Bollobás, Modern Graph Theory, Springer-Verlag, 1998.
  • J. Bondy and P. Erdős, Ramsey numbers for cycles in graphs, J. Combin. Theory Ser. B, 14 (1973), 46-54.
  • J. Bondy and M. Simonovits, Cycles of even length in graphs, J. Combin. Theory Ser. B, 16 (1974), 97–105.
  • F. Chung and R. Graham, On multicolor Ramsey numbers for complete bipartite graphs, J. Combin. Theory Ser. B, 18 (1975), 164–169.
  • F. Chung and R. Graham, Erdős on Graphs, His Legacy of Unsolved Problems, A K Peters, Wellesley, 1999.
  • G. Exoo, A lower bound for Schur numbers and multicolor Ramsey numbers, Electron. J. Combin. 1 (1994), # R8.
  • R. Faudree and R. Schelp, All Ramsey numbers for cycles in graphs, Discrete Math., 8 (1974), 313-329.
  • A. Figaj and T. Łuczak, The Ramsey numbres for a triple of long even cycles, J. Combin. Theory Ser. B, 97 (2007), 584-596.
  • R. Graham, B. Rothschild, and J. Spencer, Ramsey Theory, John Wiley & Sons, 1980.
  • A. Gyárfás, M. Ruszinkó, G. Sárközy and E. Szemerédi, Three-color Ramsey numbres for paths, Combinatorica, 27 (2007), 35-69.
  • R. Irving, Generalized Ramsey numbers for small graphs, Discrete Math., 9 (1974), 251–264.
  • Y. Li, The multi-color Ramsey number of an odd cycle, submitted.
  • Y. Li and K. Lih, Multi-color Ramsey numbers of even cycles, European J. Combin., to appear.
  • Y. Li and W. Zang, The independence number of graphs with a forbidden cycle and Ramsey numbers, J. Comb. Optim., 7 (2003), 353-359.
  • T. Łuczak, $R(C_n,C_n,C_n)\le (4+o(1))n$, J. Combin. Theory Ser. B, 75 (1999), 174-187.
  • V. Rosta, On a Ramsey type problem of J.A. Bondy and P. Erdős, I & II, J. Combin. Theory Ser. B, 15 (1973), 94-120.
  • H. Wan, Upper bounds for Ramsey numbers $R(3,3,\ldots,3)$ and Schur Numbers, J. Graph Theory, 26 (1997), 119-122.
  • R. Wenger, Extremal graphs with no $C^4$'s, $C^6$'s, or $C^{10}$'s J. Combin. Theory Ser. B, 52 (1991), 113–116.