Let , , ..., be a -Edge coloring of the Complete Graph , where
for each , 2, ..., t, is the spanning Subgraph of consisting of all Edges colored with the th color. The irredundant Ramsey number
is the smallest Integer
such that for any -Edge coloring of , the Complement Graph
has an irredundant set of size for at least one , ..., . Irredundant Ramsey numbers were introduced by
Brewster et al. (1989) and satisfy
Bounds | Reference | |
6 | Brewster et al. 1989 | |
8 | Brewster et al. 1989 | |
12 | Brewster et al. 1989 | |
15 | Brewster et al. 1990 | |
18 | Chen and Rousseau 1995, Cockayne et al. 1991 | |
13 | Cockayne et al. 1992 | |
13 | Cockayne and Mynhardt 1994 |
References
Brewster, R. C.; Cockayne, E. J.; and Mynhardt, C. M. ``Irredundant Ramsey Numbers for Graphs.'' J. Graph Theory
13, 283-290, 1989.
Brewster, R. C.; Cockayne, E. J.; and Mynhardt, C. M. ``The Irredundant Ramsey Number .'' Quaest. Math.
13, 141-157, 1990.
Chen, G. and Rousseau, C. C. ``The Irredundant Ramsey Number .'' J. Graph. Th. 19, 263-270, 1995.
Cockayne, E. J.; Exoo, G.; Hattingh, J. H.; and Mynhardt, C. M. ``The Irredundant Ramsey Number .''
Util. Math. 41, 119-128, 1992.
Cockayne, E. J.; Hattingh, J. H.; and Mynhardt, C. M. ``The Irredundant Ramsey Number .'' Util. Math.
39, 145-160, 1991.
Cockayne, E. J. and Mynhardt, C. M. ``The Irredundant Ramsey Number .'' J. Graph. Th. 18, 595-604, 1994.
Hattingh, J. H. ``On Irredundant Ramsey Numbers for Graphs.'' J. Graph Th. 14, 437-441, 1990.
Mynhardt, C. M. ``Irredundant Ramsey Numbers for Graphs: A Survey.'' Congres. Numer. 86, 65-79, 1992.
© 1996-9 Eric W. Weisstein