The expected number of vertices that remain joined to the root vertex s of a rooted graph Gs when edges are prone to fail is a polynomial EV (Gs; p) in the edge probability p that depends on the location of s. We show that optimal locations for the root can vary arbitrarily as p varies from 0 to 1 by constructing a graph in which every permutation of k specified vertices is the ‘optimal’ orderi...

Graph-indexed random walks (or equivalently M -Lipschitz mappings of graphs) are a generalization of standard random walk on Z. For M ∈ N, an M-Lipschitz mapping of a connected rooted graph G = (V,E) is a mapping f : V → Z such that root is mapped to zero and for every edge (u, v) ∈ E we have |f(u) − f(v)| ≤ M . We study two natural problems regarding graph-indexed random walks. 1. Computing th...

In a rooted graph, a vertex is designated as its root. An outerplanar graph is represented by a plane embedding such that all vertices appear along its outer boundary. Two different plane embeddings of a rooted outerplanar graphs are called symmetric copies. Given integers n ≥ 3 and g ≥ 3, we give an O(n)-space and O(1)-time delay algorithm that enumerates all biconnected rooted outerplanar gra...

A tree T of order n is called k-placement if there are k edge-disjoint copies of T into K_{n}. In this paper we prove some results about 4-placement of rooted trees.

Rooted triplets are becoming one of the important types of input for reconstructing 1 rooted phylogenies. A rooted triplet is a phylogenetic tree on three leaves and shows the 2 evolutionary relationship of the corresponding three species. In this paper, we investigate the 3 problem of inferring the maximum consensus evolutionary tree from a set of rooted triplets. 4 The mentioned problem is kn...

Electron spin resonance (ESR) measurement data of 98 teeth from atomic-bomb survivors who received various radiation doses were analyzed in terms of possible solar light exposure by tooth position. Each tooth was divided into buccal and lingual parts for independent ESR measurement. We found that average buccal doses were larger than their corresponding lingual doses by 0.48 +/- 0.30 Gy (first ...

Rooted triplets are becoming one of the most important types of input for reconstructing rooted phylogenies. A rooted triplet is a phylogenetic tree on three leaves and shows the evolutionary relationship of the corresponding three species. In this paper, we investigate the problem of inferring the maximum consensus evolutionary tree from a set of rooted triplets. This problem is known to be AP...