GENERALIZED RAMSEY NUMBERS FOR PATHS IN 2-CHROMATIC GRAPHS

• Published in: International Journal of Mathematics and Mathematical Sciences Vol. 1986; no. 2; pp. 273 - 276
• Main Authors: Meenakshi, R., Sundararaghavan, P. S.
• Format: Journal Article
• Language: English
• Published: Hindawi Limiteds 1986; Wiley
• Subjects: colored graph; d-chromatic Ramsey number; generalized Ramsey number; Ramsey number; Ramsey Number; Generalized Ramsey Number; d-Chromatic Ramsey number; Colored Graph
• ISSN: 0161-1712; 1687-0425
• DOI: 10.1155/S0161171286000339

Chung and Liu have defined the d-chromatic Ramsey number as follows. Let l≤d≤c and let = (_d^c). Let 1,2, …, t be the ordered subsets of d colors chosen from c distinct colors. Let G_1,G_2,...,G_t be graphs. The d-chromatic Ramsey number c denoted by r_d^c(G_1,G_2, … G_t) is defined as the least number p such that, if the edges of the complete graph K_p are colored in any fashion with c colors, then for some i, the subgraph whose edges are colored in the ith subset of colors contains a G_i. In this paper it is shown that r_2^3(P_i,P_j,P_k) [(4k+2j+i-2)/6] where i≤j≤k＜r(P)i,P_j) r_2^3 stands for a generalized Ramsey number on a 2-colored graph and P. is a path of order i.