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# 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

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## 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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Irredundant Ramsey Number

## Cite this as:

Weisstein, Eric W. "Irredundant Ramsey Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IrredundantRamseyNumber.html