Boxicity of Leaf Powers

dc.creatorChandran, L. Sunil
dc.creatorFrancis, Mathew C.
dc.creatorMathew, Rogers
dc.date2009-02-20
dc.date.accessioned2026-07-07T12:45:00Z
dc.date.available2026-07-07T12:45:00Z
dc.descriptionThe 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.
dc.identifierhttps://arxiv.org/abs/0902.3551
dc.identifierhttp://arxiv.org/abs/0902.3551
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220962
dc.subjectCombinatorics
dc.subject05C62 (Primary) 05C05 (Secondary)
dc.titleBoxicity of Leaf Powers
dc.typetext

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