Trees in Polyhedral Graphs
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 731-736

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A graph is said to be d-polyhedral provided it is isomorphic with the graph formed by the vertices and edges of a d-dimensional bounded (convex) polyhedron (d-polyhedron). A k-tree is a connected acyclic graph in which each vertex is of valence ⩽k.
Barnette, David. Trees in Polyhedral Graphs. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 731-736. doi: 10.4153/CJM-1966-073-4
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