A graph G is a 2-tree if G = K3, or G has a vertex v of degree 2, whose neighbors are adjacent, and G \ v is a 2-tree. A characterization of the degree sequences of 2-trees is given. This characterization yields a linear-time algorithm for recognizing and realizing degree sequences of 2-trees.

Additional Metadata
Keywords 2-tree, Degree sequence, Graphical degree sequence, K-tree, Series-parallel graph, Treewidth
Persistent URL dx.doi.org/10.1002/jgt.20302
Journal Journal of Graph Theory
Citation
Bose, P, Dujmović, V, Krizanc, D. (Danny), Langerman, S. (Stefan), Morin, P, Wood, D, & Wuhrer, S. (Stefanie). (2008). A characterization of the degree sequences of 2-trees. In Journal of Graph Theory (Vol. 58, pp. 191–209). doi:10.1002/jgt.20302