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
 |
For a summary, see Mynhardt (1992).
 | 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 |
." 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.