Geodesic
On spanning trees without vertices of degree 2 in plane triangulations
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part X, Tome 475 (2018), pp. 93-98

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Let $G$ be a $2$-connected plane graph such that at most one its face is not a triangle. It is proved that $G$ has a spanning tree without vertices of degree $2$. 
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     author = {D. V. Karpov},
     title = {On spanning trees without vertices of degree 2 in plane triangulations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {93--98},
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     volume = {475},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_475_a3/}
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D. V. Karpov. On spanning trees without vertices of degree 2 in plane triangulations. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part X, Tome 475 (2018), pp. 93-98. http://geodesic.mathdoc.fr/item/ZNSL_2018_475_a3/