An st-path is a path with the end-vertices s and t. An s-path is a path with an end-vertex s. The results of this paper include necessary and sufficient conditions for a {claw, net}-free graph G with s, t ∈ V (G) and e ∈ E(G) to have (1) a Hamiltonian s-path, (2) a Hamiltonian st-path, (3) a Hamiltonian sand st-paths containing e when G has connectivity one, and (4) a Hamiltonian cycle containi...

An st-path is a path with the end-vertices s and t. An s-path is a path with an end-vertex s. The results of this paper include necessary and sufficient conditions for a {claw, net}-free graph G with s, t ∈ V (G) and e ∈ E(G) to have (1) Hamiltonian s-path, (2) a Hamiltonian st–path, (3) a Hamiltonian sand st-paths containing e when G has connectivity one, and (4) a Hamiltonian cycle containing...

In the 14 July 1997, issue of Lancet, Schlemper et al. [1] reported a study in which four Japanese and four Western pathologists (from the United States, Canada, Germany, and Finland) compared their diagnoses of gastric biopsy and resection specimens having epithelial lesions ranging from reactive, through preneoplastic, to invasive carcinoma. These pathologists independently classified microsc...

We design the rst eecient parallel algorithm for computing the minimal elimination ordering (MEO) of an arbitrary graph. The algorithm works in O(log 3 n) parallel time and O(nm) processors on a CREW PRAM, for an n-vertex, m-edge graph, and is optimal up to a polylogarithmic factor with respect to the best sequential algorithm of Rose, Tarjan and Lueker ((RTL 76]). The MEO problem for arbitrary...

We consider only finite undirected graphs without loops or multiple edges. Notation or terms not defined here can be found in [1]. Let G be a graph and let S £; V( G). The subgraph (S) induced by S is the graph with vertex set Sand Whose edge set consists of those edges of G incident with two vertices of S. The distance d(u, v) between vertices u and v in a connected graph G is the minimum numb...

A general overview of the problem of automatically generating aesthetically pleasing drawings of graphs is presented. Requirements particular to diagrams in Rational Rose is discussed. The Sugiyama layout algorithm and the Spring Embedder algorithm together with a number of proposed modifications and improvements to these algorithms are discussed. Examples of drawings generated by these algorit...