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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