## Graphs of exact colorings ★★

Author(s):

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 .

Keywords:

## Imbalance conjecture ★★

Author(s): Kozerenko

**Conjecture**Suppose that for all edges we have . Then is graphic.

Keywords: edge imbalance; graphic sequences