## Chromatic number of $\frac{3}{3}$-power of graph ★★

Author(s):

Let be a graph and . The graph is defined to be the -power of the -subdivision of . In other words, .

**Conjecture**Let be a graph with . Then .

Keywords:

## KPZ Universality Conjecture ★★★

Author(s):

**Conjecture**Formulate a central limit theorem for the KPZ universality class.

Keywords: KPZ equation, central limit theorem

## 3-Edge-Coloring Conjecture ★★★

Author(s): Arthur; Hoffmann-Ostenhof

**Conjecture**Suppose with is a connected cubic graph admitting a -edge coloring. Then there is an edge such that the cubic graph homeomorphic to has a -edge coloring.

Keywords: 3-edge coloring; 4-flow; removable edge