Structure and linear-time recognition of 4-leaf powers

Authors:
Andreas Brandstädt;Van Bang Le;R. Sritharan
Affiliations:
Universität Rostock, Rostock, Germany;Universität Rostock, Rostock, Germany;The University of Dayton, Dayton, OH
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2008

Citing 10
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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(n3)-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.