# Graphs of exact colorings

Conjecture For , let be the statement that given any exact -coloring of the edges of a complete countably infinite graph (that is, a coloring with colors all of which must be used at least once), there exists an exactly -colored countably infinite complete subgraph. Then is true if and only if , , or .

Stacey and Weidl have shown that given , there is an integer such that is false for all .

* M. Erickson, ``A Conjecture Concerning Ramsey's Theorem,'' Discrete Mathematics 126, 395--398 (1994); MR 95b:05209

A. Stacey and P. Weidl, "The Existence of Exactly m-Coloured Complete Subgraphs," J. of Combinatorial Theory, Series B 75, 1-18 (1999)

* indicates original appearance(s) of problem.

## Bibliography

* indicates original appearance(s) of problem.