Irredundant Ramsey Number
المؤلف:
Brewster, R. C.; Cockayne, E. J.; and Mynhardt, C. M
المصدر:
"Irredundant Ramsey Numbers for Graphs." J. Graph Theory 13
الجزء والصفحة:
...
28-3-2022
1928
Irredundant Ramsey Number
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 |
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.
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