International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 273-276
Generalized Ramsey numbers for paths in -chromatic graphs
1Mathematics Department, The University of Toledo, Toledo 43606, Ohio, USA
2Computer Systems Department, The University of Toledo, Toledo 43606, Ohio, USA
Received 26 April 1984; Revised 6 January 1985
Copyright © 1986 R. Meenakshi and P. S. Sundararaghavan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 .