Vertex-connectivity conjecture for cages

Prove that every simple $(k,g)$-cage is $k$-connected.

Background

The paper distinguishes ordinary vertex-connectivity from edge-connectivity and summarizes prior results giving lower bounds on the connectivity of cages for certain degree and girth ranges. It records a broader conjecture attributed to Fu et al. asserting that all simple cages attain the maximum possible vertex-connectivity allowed by regularity.

References

Fu et al. conjectured that all simple $(k, g)$-cages are $k$-connected.

— Cages and cyclic connectivity  (2503.07400 - Lukoťka et al., 10 Mar 2025) in Section 1, Introduction