Geodesic
On Robillard′s Bounds for Ramsey Numbers
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 437-440

Voir la notice de l'article provenant de la source Cambridge University Press

A recent issue of the Bulletin contained a paper by Robillard [13] in which results from the theory of confounded factorial designs were used to obtain some lower bounds for Ramsey numbers. We shall derive, by more elementary methods, bounds which are much better than Robillard's in every example which he considered. 
Kalbfleisch, J. G. On Robillard′s Bounds for Ramsey Numbers. Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 437-440. doi: 10.4153/CMB-1971-076-5
@article{10_4153_CMB_1971_076_5,
     author = {Kalbfleisch, J. G.},
     title = {On {Robillard's} {Bounds} for {Ramsey} {Numbers}},
     journal = {Canadian mathematical bulletin},
     pages = {437--440},
     year = {1971},
     volume = {14},
     number = {3},
     doi = {10.4153/CMB-1971-076-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-076-5/}
}
TY  - JOUR
AU  - Kalbfleisch, J. G.
TI  - On Robillard′s Bounds for Ramsey Numbers
JO  - Canadian mathematical bulletin
PY  - 1971
SP  - 437
EP  - 440
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-076-5/
DO  - 10.4153/CMB-1971-076-5
ID  - 10_4153_CMB_1971_076_5
ER  - 
%0 Journal Article
%A Kalbfleisch, J. G.
%T On Robillard′s Bounds for Ramsey Numbers
%J Canadian mathematical bulletin
%D 1971
%P 437-440
%V 14
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-076-5/
%R 10.4153/CMB-1971-076-5
%F 10_4153_CMB_1971_076_5

[1] 1. Erdös, P., Some remarks on the theory of graphs, Bull. Amer. Math. Soc. 53 (1947), 292-294. Google Scholar

[2] 2. Erdös, P., Graph theory and probability II, Canad. J. Math. 13 (1961), 346-352. Google Scholar

[3] 3. Erdös, P. A., Hajnal, , and Rado, R., Partition relations for cardinal numbers, Acta. Math. Acad. Sci. Hungar. 16 (1965), 93-196. Google Scholar

[4] 4. Giraud, Guy, Sur les nombres de Ramsey ternaires-bicolores de la diagonale, C. R. Acad. Se. Paris, Sér. A, 268 (1969), 85-87. Google Scholar

[5] 5. Graver, J. E. and Yackel, J., Some graph theoretic results associated with Ramsey's theorem, J. Comb. Theory 4 (1968), 125-175. Google Scholar

[6] 6. Greenwood, R. E. and Gleason, A. M., Combinatorial relations and chromatic graphs, Canad. J. Math. 7 (1955), 1-7. Google Scholar

[7] 7. Isbell, John R., N(A, 4; 3)≥ 13, J. Comb. Theory 6 (1969), p. 210. Google Scholar

[8] 8. Kalbfleisch, J. G., Chromatic graphs and Ramsey's theorem, Ph.D. thesis, Univ. of Waterloo, 1966. Google Scholar

[9] 9. Kalbfleisch, J. G., On the Ramsey number N(4, 4; 3), Recent progress in combinatorics, (edited by W. T. Tutte), Academic Press, New York, 1969, 273-282. Google Scholar

[10] 10. Kéry, G., Ramsey egy gráfélmeleti tételéröl, Mat. Lapok 15 (1964), 202-224. Google Scholar

[11] 11. Krieger, Michael M., An inequality for higher Ramsey numbers, Notices Amer. Math. Soc. 15 (1968), p. 1035, Abstract No. 662–18. Google Scholar

[12] 12. Ramsey, F. P., On a problem in formal logic, Proc. London Math. Soc. (2) 30 (1930), 264-286. Google Scholar

[13] 13. Robillard, Pierre, Lower bounds for the Ramsey numbers, Canad. Math. Bull. 13 (1970), 227-229. Google Scholar

[14] 14. Walker, K., Dichromatic graphs and Ramsey numbers, J. Comb. Theory 5 (1968), 238-243. Google Scholar

Cité par Sources :