A Characterization of the Degree Sequences of 2-Trees
Prosenjit Bose, Vida Dujmovi\'c, Danny Krizanc, Stefan Langerman, Pat, Morin, David R. Wood, Stefanie Wuhrer
TL;DR
This paper provides a complete characterization of degree sequences for 2-trees, enabling efficient recognition and realization algorithms, which advances understanding of their structural properties.
Contribution
It introduces a new characterization of 2-tree degree sequences and develops a linear-time algorithm for recognition and realization.
Findings
Characterization of 2-tree degree sequences
Linear-time recognition algorithm
Efficient realization of degree sequences
Abstract
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.
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