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Boxicity of Leaf Powers

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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.

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Authors and Affiliations

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

    L. Sunil Chandran, Mathew C. Francis & Rogers Mathew

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  1. L. Sunil Chandran
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  2. Mathew C. Francis
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  3. Rogers Mathew
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Correspondence to L. Sunil Chandran.

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Chandran, L.S., Francis, M.C. & Mathew, R. Boxicity of Leaf Powers. Graphs and Combinatorics 27, 61–72 (2011). https://doi.org/10.1007/s00373-010-0962-5

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  • DOI: https://doi.org/10.1007/s00373-010-0962-5

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