Let ,
,
...,
be a -graph edge coloring of the complete
graph ,
where for each ,
2, ..., t,
is the spanning subgraph of consisting of all graph edges
colored with the th color. The irredundant Ramsey number is the smallest integer
such that for any -graph edge coloring of ,
the graph complement has an irredundant set
of size
for at least one , ..., . Irredundant Ramsey numbers were introduced by Brewster et
al. (1989) and satisfy
Brewster, R. C.; Cockayne, E. J.; and Mynhardt, C. M. "Irredundant Ramsey Numbers for Graphs." J. Graph Theory13,
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.