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Boxicity of Leaf Powers
- Publication Year :
- 2009
-
Abstract
- The boxicity of a graph G, denoted as box(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 a subclass of strongly chordal graphs and are used in the construction of phylogenetic trees in evolutionary biology. We show that for a k-leaf power G, box(G)\leq 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 exists strongly chordal graphs with arbitrarily high boxicity which is somewhat counterintuitive.
- Subjects :
- Mathematics - Combinatorics
05C62 (Primary) 05C05 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.0902.3551
- Document Type :
- Working Paper