Constructive lower bounds on classical multicolor ramsey numbers

Electronic Journal of Combinatorics

Volumn 11, Issue 1 R, 2004, Pages

  Xiaodong, Xu ^a   Zheng, Xie ^a   Exoo, Geoffrey ^b   Radziszowski, Stanisław P ^c  

^a NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY   (China)

^b INDIANA STATE UNIVERSITY   (United States)

^c Rochester Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042675938     PISSN: 10778926     EISSN: None     Source Type: Journal    
DOI: 10.37236/1788     Document Type: Article

References (29)

1. H. L. Abbott, Ph. D. thesis, University of Alberta, Edmonton, 1965.
2. H. L. Abbott and D. Hanson, A Problem of Schur and Its Generalizations, Acta Arithmetica, 20 (1972) 175-187.
3. H. L. Abbott and L. Moser, Sum-Free Sets of Integers, Acta Arithmetica, 11 (1966) 393-396.
4. R. Beekman, personal communication (2000).
5. F. R. K. Chung, On the Ramsey Numbers N(3, 3, ..., 3; 2), Discrete Mathematics, 5 (1973) 317-321.
6. F. R. K. Chung and C. M. Grinstead, A Survey of Bounds for Classical Ramsey Numbers, Journal of Graph Theory, 7 (1983) 25-37.
7. 3, Electronic Journal of Combinatorics, #R8, 1 (1994), 3 pages, http://www.combinatorics.org.
8. G. Exoo, Some New Ramsey Colorings (2003), constructions available at http://isu.indstate.edu/ge/RAMSEY.
9. S. Fettes, R. L. Kramer and S. P. Radziszowski, An Upper Bound of 62 on the Classical Ramsey Number R(3, 3, 3, 3), to appear in Ars Combinatoria.
10. H. Fredricksen, Five Sum-Free Sets, Congressus Numerantium, 14 (1975) 309-314.
11. H. Fredricksen and M. M. Sweet, Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers, Electronic Journal of Combinatorics, #R32, 7 (2000), 9 pages, http://www.combinatorics.org.
12. G. Giraud, Une généralisation des nombres et de l'inégalité de Schur, C.R. Acad. Sc. Paris, Série A, 266 (1968) 437-440.
13. G. Giraud, Minoration de certains nombres de Ramsey binaires par les nombres de Schur généralisés, C.R. Acad. Sc. Paris, Série A, 266 (1968) 481-483.
14. R. E. Greenwood and A. M. Gleason, Combinatorial Relations and Chromatic Graphs, Canadian Journal of Mathematics, 7 (1955) 1-7.
15. R. Hill and R. W. Irving, On Group Partitions Associated with Lower Bounds for Symmetric Ramsey Numbers, European Journal of Combinatorics, 3 (1982) 35-50.
16. J. G. Kalbfleisch, Construction of Special Edge-Chromatic Graphs, Canadian Mathematical Bulletin, 8 (1965) 575-584.
17. J. G. Kalbfleisch, Chromatic Graphs and Ramsey's Theorem, Ph.D. thesis, University of Waterloo, January 1966.
18. J. G. Kalbfleisch and R. G. Stanton, On the Maximal Triangle-Free Edge-Chromatic Graphs in Three Colors, Journal of Combinatorial Theory, 5 (1968) 9-20.
19. D. L. Kreher, Li Wei and S. P. Radziszowski, Lower Bounds for Multi-Colored Ramsey Numbers From Group Orbits, Journal of Combinatorial Mathematics and Combinatorial Computing, 4 (1988) 87-95.
20. R. Mathon, Lower Bounds for Ramsey Numbers and Association Schemes, Journal of Combinatorial Theory, Series B, 42 (1987) 122-127.
21. K. Piwakowski and S. P. Radziszowski, Towards the Exact Value of the Ramsey Number R(3, 3, 4), Congressus Numerantium, 148 (2001) 161-167.
22. S. P. Radziszowski, Small Ramsey numbers, Electronic Journal of Combinatorics, Dynamic Survey 1, revision #9, July 2002, http://www. combinatorics.org.
23. A. Robertson, New Lower Bounds for Some Multicolored Ramsey Numbers, Electronic Journal of Combinatorics, #R12, 6 (1999), 6 pages, http://www.combinatorics.org.
24. A. Robertson, New Lower Bounds Formulas for Multicolored Ramsey Numbers, Electronic Journal of Combinatorics, #R13, 9 (2002), 6 pages, http://www.combinatorics.org.
25. J. B. Shearer, Lower Bounds for Small Diagonal Ramsey Numbers, Journal of Combinatorial Theory, Series A, 42 (1986) 302-304.
26. Song En Min, New Lower Bound Formulas for the Ramsey Numbers N(k, k, ..., k; 2) (in Chinese), Mathematica Applicata, 6 (1993) suppl., 113-116.
27. Song En Min, An Investigation of Properties of Ramsey Numbers (in Chinese), Mathematica Applicata, 7 (1994) 216-221.
28. Xu Xiaodong, Classical Ramsey Theory and Its Application (in Chinese), manuscript (2003).
29. Xu Xiaodong, Xie Zheng and S. P. Radziszowski, A Constructive Approach for the Lower Bounds on the Ramsey Numbers R(s, t), to appear in the Journal of Graph Theory.