Department of Computer Science and AutomationIndian Institute of Science

Mathew C. Francis

Department of Computer Science and AutomationIndian Institute of Science

Rogers Mathew

Department of Computer Science and AutomationIndian Institute of Science

Original Paper

First Online:

Received:

Revised:

DOI:
10.1007/s00373-010-0962-5

Cite this article as:

Chandran, L.S., Francis, M.C. & Mathew, R. Graphs and Combinatorics (2011) 27: 61. doi:10.1007/s00373-010-0962-5

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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) ≤ 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.