Ingleton's critical-graph excluded-minor conjecture

Let $\Delta$ be a critical graph with no obstructions, and let $M(\Delta)$ be the matroid whose lattice of cyclic flats is $\mathcal{Z}_\Delta$.

Ingleton's critical-graph conjecture. If $\Delta$ is a critical graph with no obstructions, then $M(\Delta)$ is an excluded minor for $\mathcal{BO}$.

This reformulates a conjecture attributed to Ingleton. The paper proves a special case, while the assertion for all critical graphs with no obstructions remains open.