Jackson's Tutte-cycle conjecture for 2-connected claw-free graphs

A graph is claw-free if it has no induced subgraph isomorphic to $K_{1,3}$. A graph is 2-connected if it is connected and remains connected after deleting any one vertex. A Tutte cycle is a cycle $C$ such that every component of $G-V(C)$ has at most three neighbours on $C$.

Jackson's conjecture. Every $2$-connected claw-free graph has a Tutte cycle.

This is presented as an equivalent formulation of Thomassen's open conjecture on Hamilton cycles in 4-connected line graphs. The equivalence is obtained using the closure technique, but the conjecture itself remains unresolved.