R. Meenakshi, P. S. Sundararaghavan, "Generalized Ramsey numbers for paths in -chromatic graphs", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 560279, 4 pages, 1986. https://doi.org/10.1155/S0161171286000339
Generalized Ramsey numbers for paths in -chromatic graphs
Chung and Liu have defined the -chromatic Ramsey number as follows. Let and let . Let be the ordered subsets of colors chosen from distinct colors. Let be graphs. The -chromatic Ramsey number denoted by is defined as the least number such that, if the edges of the complete graph are colored in any fashion with colors, then for some , the subgraph whose edges are colored in the th subset of colors contains a . In this paper it is shown that where , stands for a generalized Ramsey number on a -colored graph and is a path of order .
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