# coloring

## Reed's omega, delta, and chi conjecture ★★★

Author(s): Reed

For a graph , we define to be the maximum degree, to be the size of the largest clique subgraph, and to be the chromatic number of .

**Conjecture**for every graph .

Keywords: coloring

## Grunbaum's Conjecture ★★★

Author(s): Grunbaum

**Conjecture**If is a simple loopless triangulation of an orientable surface, then the dual of is 3-edge-colorable.

## Linial-Berge path partition duality ★★★

**Conjecture**The minimum -norm of a path partition on a directed graph is no more than the maximal size of an induced -colorable subgraph.

Keywords: coloring; directed path; partition