Affiliation:
1. Universität Rostock, Rostock, Germany
2. The University of Dayton, Dayton, OH
Abstract
A graph
G
is the
k-leaf power
of a tree
T
if its vertices are leaves of
T
such that two vertices are adjacent in
G
if and only if their distance in
T
is at most
k
. Then
T
is a
k-leaf root
of
G
. This notion was introduced and studied by Nishimura, Ragde, and Thilikos [2002], motivated by the search for underlying phylogenetic trees. Their results imply an
O
(
n
3
)-time recognition algorithm for 4-leaf powers. Recently, Rautenbach [2006] as well as Dom et al. [2005] characterized 4-leaf powers without true twins in terms of forbidden subgraphs. We give new characterizations for 4-leaf powers and squares of trees by a complete structural analysis. As a consequence, we obtain a conceptually simple linear-time recognition of 4-leaf powers.
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Reference21 articles.
1. Computing Phylogenetic Roots with Bounded Degrees and Errors
2. Dahlhaus E. and Duchet P. 1987. On strongly chordal graphs. Ars Combin. 24 B 23--30. Dahlhaus E. and Duchet P. 1987. On strongly chordal graphs. Ars Combin. 24 B 23--30.
3. Extending the Tractability Border for Closest Leaf Powers
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