منابع مشابه
Boxicity of Leaf Powers
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 axisparallel 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 power...
متن کاملOn Leaf Powers
For an integer k, a tree T is a k-leaf root of a finite simple undirected graph G = (V,E) if the set of leaves of T is the vertex set V of G and for any two vertices x, y ∈ V , x 6= y, xy ∈ E if and only if the distance of x and y in T is at most k. Then graph G is a k-leaf power if it has a k-leaf root. G is a leaf power if it is a k-leaf power for some k. This notion was introduced and studie...
متن کاملOn Graph Powers for Leaf-Labeled Trees
We extend the well-studied concept of a graph power to that of a k-leaf power G of a tree T : G is formed by creating a node for each leaf in the tree and an edge between a pair of nodes if and only if the associated leaves are connected by a path of length at most k. By discovering hidden combinatorial structure of cliques and neighborhoods, we have developed polynomial-time algorithms that, f...
متن کاملStrictly chordal graphs are leaf powers
A fundamental problem in computational biology is the phylogeny reconstruction for a set of specific organisms. One of the graph theoretical approaches is to construct a similarity graph on the set of organisms where adjacency indicates evolutionary closeness, and then to reconstruct a phylogeny by computing a tree interconnecting the organisms such that leaves in the tree are labeled by the or...
متن کاملTowards a Characterization of Leaf Powers by Clique Arrangements
The class Lk of k-leaf powers consists of graphs G = (V,E) that have a k-leaf root, that is, a tree T with leaf set V , where xy ∈ E, if and only if the T -distance between x and y is at most k. Structure and linear time recognition algorithms have been found for 2-, 3-, 4-, and, to some extent, 5-leaf powers, and it is known that the union of all k-leaf powers, that is, the graph class L = ⋃∞ ...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2010
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2010.04.027