A Characterization of the Degree Sequences of 2-Trees
  A graph G is a 2-tree if G=K_3, or G has a vertex v of degree 2, whose neighbours are adjacent, and G\v{i}s 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. 
Prosenjit Bose, Vida Dujmovi\'c, Danny Krizanc, Stefan Langerman, Pat   Morin, David R. Wood, Stefanie Wuhrer