# Three-chromatic (0,2)-graphs

**Question**Are there any (0,2)-graphs with chromatic number exactly three?

A (0,2)-graph is a graph such that every pair of distinct vertices has either 0 or 2 common neighbours. It is fairly easy to see that a (0,2)-graph is necessarily regular and a variety of other properties can be shown to hold. Although (0,2)-graphs with chromatic number 2, 4 and 5 are known it is open as to whether there can be any (0,2)-graphs with chromatic number exactly three.

## Bibliography

*[P] Payan, Charles: On the chromatic number of cube-like graphs, Discrete Math. 103 (1992), no. 3, 271--277.

* indicates original appearance(s) of problem.

## Finite Three-Chromatic (0,2)-graphs

An infinite three-chromatic (0, 2)-graph is easy to construct. See Payan.