Plane Embeddings of 2-Trees and Biconnected Partial 2-Trees
Andrzej Proskurowski, Maciej M. Sysło, Paweł Winter · SIAM Journal on Discrete Mathematics · 1996
We consider different plane embeddings of partial 2-trees and give an efficient algorithm constructing a minimum cardinality cover of faces, where each face is covered by exactly one vertex. These tasks are facilitated by a unique tree representation of plane embeddings of 2-trees.