We consider the problems of finding spanning k-caterpillars and k-trees in graphs. We first show that the problem of whether a graph has a spanning kcaterpillar is NP-complete, for all k ≥ 1. Then we give a linear time algorithm for finding a spanning 1-caterpillar in a graph with treewidth k. Also, as a generalized versions of the depth-first search and the breadth-first search algorithms, we ...

The reciprocal complementary Wiener number of a connected graph G is defined as ( ) { } ( ) ( ) | ∑ u v V G RCW G d d u v G ⊆ = + − , 1 1 , where ( ) V G is the vertex set. ( ) | d u v G , is the distance between vertices u and v, and d is the diameter of G. A tree is known as a caterpillar if the removal of all pendant vertices makes it as a path. Otherwise, it is called a non-caterpillar. Amo...

We present a novel, yet simple, technique for the speciication of context in structured documents that we call caterpillar expressions. Although we are applying this technique in the speciication of context-dependent style sheets for HTML, XML, and SGML documents, it is clear that it can be used in other environments such as query speciication for structured documents and for computer program t...

We study the Minimum Spanning Caterpillar Problem (MSCP) in a graph where each edge has two costs, spine (path) cost and leaf cost, depending on whether it is used as a spine or a leaf edge. The goal is to find a spanning caterpillar in which the sum of its edge costs is the minimum. We show that the problem has a linear time algorithm when a tree decomposition of the graph is given as part of ...

In the first part of this paper we present the first steps towards providing low-risk and economically feasible network data transfer services. We introduce three types of data transfer services and present general guidelines and algorithms for managing service prices, risks and schedules. In the second part of the paper we solve two packet scheduling cost optimization problems and present effi...

A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f ...

BACKGROUND Approximately 150 species of Lepidoptera have been described as causing damage to human skin. One of these species is the pine processionary caterpillar, which is responsible for dermatitis, contact urticaria, ocular lesions and rarely respiratory signs and anaphylactic reactions through IgE-mediated or non-IgE-mediated mechanisms. We report a pediatric case of severe orofacial edema...

We establish that regularly extended two-way nondeterministic tree automata with unranked alphabets have the same expressive power as regularly extended nondeterministic tree automata with unranked alphabets. We obtain this result by establishing regularly extended versions of a congruence on trees and of a congruence on, so called, views. Our motivation for the study of these tree models is th...

We establish that regularly extended two-way nondeterministic tree automata with un-ranked alphabets have the same expressive power as regularly extended nondeterministic tree automata with unranked alphabets. We obtain this result by establishing regularly extended versions of a congruence on trees and of a congruence on, so called, views. Our motivation for the study of these tree models is t...