A Characterization of the degree sequences of 2‐trees
Prosenjit K. Bose, Vida Dujmović, Danny Kriz̧anc, Stefan Langerman, Pat Morin, David R. Wood, Stefanie Wuhrer · Journal of Graph Theory · 2008
Abstract 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. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:191‐209, 2008