Discussiones Mathematicae Graph Theory 25(1-2) (2005)
57-65
doi: 10.7151/dmgt.1260
Tomasz Dzido
Department of Computer Science
University of Gdańsk
Wita Stwosza 57, 80-952 Gdańsk, Poland
e-mail: tdz@math.univ.gda.pl
Keywords: edge coloring, Ramsey number.
2000 Mathematics Subject Classification: 05C15, 05C55.
[1] | J. Arste, K. Klamroth and I. Mengersen, Three color Ramsey numbers for small graphs, Utilitas Mathematica 49 (1996) 85-96. |
[2] | J.A. Bondy and P. Erdös, Ramsey numbers for cycles in graphs, J. Combin. Theory (B) 14 (1973) 46-54, doi: 10.1016/S0095-8956(73)80005-X. |
[3] | A. Burr and P. Erdös, Generalizations of a Ramsey-theoretic result of Chvatal, J. Graph Theory 7 (1983) 39-51, doi: 10.1002/jgt.3190070106. |
[4] | C. Clapham, The Ramsey number R(C_{4},C_{4},C_{4}), Periodica Mathematica Hungarica 18 (1987) 317-318, doi: 10.1007/BF01848105. |
[5] | T. Dzido, Computer experience from calculating some 3-color Ramsey numbers (Technical Report of Gdańsk University of Technology ETI Faculty, 2003). |
[6] | R. Faudree, A. Schelten and I. Schiermeyer, The Ramsey number R(C_{7},C_{7},C_{7}), Discuss. Math. Graph Theory 23 (2003) 141-158, doi: 10.7151/dmgt.1191. |
[7] | R.E. Greenwood and A.M. Gleason, Combinatorial relations and chromatic graphs, Canadian J. Math. 7 (1955) 1-7, doi: 10.4153/CJM-1955-001-4. |
[8] | T. Łuczak, R(C_{n},C_{n},C_{n}) ≤ (4+o(1))n, J. Combin. Theory (B) 75 (1999) 174-187. |
[9] | S.P. Radziszowski, Small Ramsey numbers, Electronic J. Combin. Dynamic Survey 1, revision #9, July 2002, http://www.combinatorics.org/. |
[10] | P. Rowlison and Y. Yang, On the third Ramsey numbers of graphs with five edges, J. Combin. Math. and Combin. Comp. 11 (1992) 213-222. |
[11] | P. Rowlison and Y. Yang, On Graphs without 6-cycles and related Ramsey numbers, Utilitas Mathematica 44 (1993) 192-196. |
[12] | D.R. Woodall, Sufficient conditions for circuits in graphs, Proc. London Math. Soc. 24 (1972) 739-755, doi: 10.1112/plms/s3-24.4.739. |
Received 30 October 2003
Revised 28 January 2005