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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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|
|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 (Formerly, School of Automation)|
|Date Deposited:||07 Feb 2011 12:30|
|Last Modified:||07 Feb 2011 12:30|
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