GENERALIZED RAMSEY NUMBERS FOR PATHS IN 2-CHROMATIC GRAPHS
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 num...
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Published in | International Journal of Mathematics and Mathematical Sciences Vol. 1986; no. 2; pp. 273 - 276 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Hindawi Limiteds
1986
Wiley |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0161-1712 1687-0425 |
DOI: | 10.1155/S0161171286000339 |