Geodesic
A note on Hamiltonian cycles in generalized Halin graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 701-704.

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We show that every 2-connected (2)-Halin graph is Hamiltonian.
Keywords: planar graphs, Halin graphs, hamiltonian cycles 
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Bojarska, Magdalena. A note on Hamiltonian cycles in generalized Halin graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 701-704. http://geodesic.mathdoc.fr/item/DMGT_2010_30_4_a13/

[1] C.A. Barefoot, Hamiltonian connectivity of the Halin graphs, in: Eighteenth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, Fla., 1987), Congr. Numer. 58 (1987) 93-102.

[2] J.A. Bondy and L. Lovasz Lengths of cycles in Halin graphs, J. Graph Theory 9 (1985) 397-410, doi: 10.1002/jgt.3190090311.