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A Characterization of the degree sequences of 2‐trees
Author(s) -
Bose Prosenjit,
Dujmović Vida,
Krizanc Danny,
Langerman Stefan,
Morin Pat,
Wood David R.,
Wuhrer Stefanie
Publication year - 2008
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20302
Subject(s) - combinatorics , mathematics , degree (music) , characterization (materials science) , vertex (graph theory) , tree (set theory) , graph , discrete mathematics , materials science , physics , acoustics , nanotechnology
A graph G is a 2‐tree if G = K 3 , 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