**Question**Is every proper vertex-minor closed class of graphs chi-bounded?

We say that a family of graphs is -*bounded* if there is a function so that for every .

If is a simple graph, a vertex minor of is any graph which can be obtained by a sequence of the following operations:

- \item delete a vertex \item choose a vertex and complement the neighborhood of (i.e. whenever are neighbors of , switch between adjacent/non-adjacent).

Dvorak and Kral [DK] showed that this conjecture is true for class of graphs of bounded rank-width, and the class of graphs having no vertex-minor isomorphic to the wheel on vertices.

## Bibliography

[DK] Z. Dvorak and D. Král. Classes of graphs with small rank decompositions are χ-bounded. European J. Combin., 33(4):679–-683, 2012. MathSciNet

* indicates original appearance(s) of problem.