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a/graphtheory posted by smh 3 weeks ago

Conjecture: If $G$ is a $4$-connected and claw-free, then $G$ is Hamiltonian. An equivalent statement is that Every $4$-connected line graph is hamiltonian, as proven by Ryjacek.

Here are some related articles/results

http://math.ucdenver.edu/~fpfender/papers/13.pdf