Boxicity of Leaf Powers
 L. Sunil Chandran,
 Mathew C. Francis,
 Rogers Mathew
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Abstract
The boxicity of a graph G, denoted as boxi(G), is defined as the minimum integer t such that G is an intersection graph of axisparallel tdimensional boxes. A graph G is a kleaf power if there exists a tree T such that the leaves of the tree correspond to the vertices of G and two vertices in G are adjacent if and only if their corresponding leaves in T are at a distance of at most k. Leaf powers are used in the construction of phylogenetic trees in evolutionary biology and have been studied in many recent papers. We show that for a kleaf power G, boxi(G) ≤ k−1. We also show the tightness of this bound by constructing a kleaf power with boxicity equal to k−1. This result implies that there exist strongly chordal graphs with arbitrarily high boxicity which is somewhat counterintuitive.
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 Title
 Boxicity of Leaf Powers
 Journal

Graphs and Combinatorics
Volume 27, Issue 1 , pp 6172
 Cover Date
 20110101
 DOI
 10.1007/s0037301009625
 Print ISSN
 09110119
 Online ISSN
 14355914
 Publisher
 Springer Japan
 Additional Links
 Topics
 Keywords

 Boxicity
 Leaf powers
 Tree powers
 Strongly chordal graphs
 Interval graphs
 Industry Sectors
 Authors

 L. Sunil Chandran ^{(1)}
 Mathew C. Francis ^{(1)}
 Rogers Mathew ^{(1)}
 Author Affiliations

 1. Department of Computer Science and Automation, Indian Institute of Science, Bangalore, 560012, India