I am currently looking into a conjecture in graph theory, known as the Jackson conjecture (1992). It says the following, in an equivalent formulation to its equivalent statement:
*Conjecture*Every 4-connected claw-free graph is Hamiltonian.
Recall that a graph is hamiltonian if a cycle visits each vertex exactly once, and that it is $n$-connected given that the deletion of those $n$ vertices keeps the graph together.
My question is, is there any reference that summarizes all of the 4-connected claw-free graphs?, i.e., is there any paper out there with a list of those graphs?