Boxicity of Leaf Powers

Chandran, Sunil L and Francis, Mathew C and Mathew, Rogers (2011) Boxicity of Leaf Powers. In: Graphs and Combinatorics, 27 (1). pp. 61-72.

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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 axis-parallel t-dimensional boxes. A graph G is a k-leaf 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 k-leaf power G, boxi(G) a parts per thousand currency sign k-1. We also show the tightness of this bound by constructing a k-leaf power with boxicity equal to k-1. This result implies that there exist strongly chordal graphs with arbitrarily high boxicity which is somewhat counterintuitive.

Item Type:	Journal Article
Publication:	Graphs and Combinatorics
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Keywords:	Boxicity;Leaf powers;Tree powers;Strongly chordal graphs; Interval graphs.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	07 Feb 2011 12:30
Last Modified:	07 Feb 2011 12:30
URI:	http://eprints.iisc.ac.in/id/eprint/35017

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