论文信息 - On Group Partitions Associated with Lower Bounds for Symmetric Ramsey Numbers

On Group Partitions Associated with Lower Bounds for Symmetric Ramsey Numbers

Most of the best available lower bounds for symmetric Ramsey numbers arise from partitions of abelian groups into classes which have a certain difference-free property and which, in addition, turn out to be images of each other under group automorphisms. We make a detailed study of group partitions having this latter property, and report the results of exhaustive searches for partitions of this type which yield improved lower bounds for certain of these Ramsey numbers.

Ray Hill | Robert W. Irving

[1] A. D. Sands. On the factorisation of finite abelian groups. III , 1957 .

[2] P. Erdös. Some remarks on the theory of graphs , 1947 .

[3] Fan Chung Graham. On the ramsey numbers N(3, 3, ...3;2) , 1973, Discret. Math..

[4] K. Walker. An Upper Bound for the Ramsey Number M(5, 4) , 1971, J. Comb. Theory, Ser. A.

[5] C. R. J. Clapham,et al. A class of self-complementary graphs and lower bounds of some ramsey numbers , 1979, J. Graph Theory.

[6] G. Hajós,et al. Sur le problème de factorisation des groupes cycliques , 1950 .

[7] J. G. Kalbfleisch,et al. On the maximal triangle-free edge-chromatic graphs in three colors , 1968 .

[8] Earl Glen Whitehead. The ramsey number N(3, 3, 3, 3; 2) , 1973, Discret. Math..

[9] Nicolette De Bruijn,et al. On the factorization of cyclic groups , 1953 .

[10] R. Greenwood,et al. Combinatorial Relations and Chromatic Graphs , 1955, Canadian Journal of Mathematics.

[11] H. Abbott,et al. Sum-free sets of integers , 1966 .

[12] Harold Fredricksen. Schur Numbers and the Ramsey Numbers N(3, 3, ..., 3; 2) , 1979, J. Comb. Theory, Ser. A.

[13] Joel H. Spencer,et al. Ramsey's Theorem - A New Lower Bound , 1975, J. Comb. Theory, Ser. A.

[14] Fan Rong K. Chung. On the ramsey numbers N(3,3,...3;2) , 1973 .