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a/graphtheory posted by smh 2 months 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:

https://link.springer.com/content/pdf/10.1007/s00373-011-1090-6.pdf

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

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