10085490
Circumferences of regular claw-free graphs
A known result obtained independently by Fan and Jung is that every 3-connected k-regular graph on n vertices contains a cycle of length at least min{3k,n}. This raises the question of how much can be said about the circumferences of 3-connected k-regular claw-free graphs. In this paper, we show that every 3-connected k-regular claw-free graph on n vertices contains a cycle of length at least min{6k-17,n}.
29060290
Hamiltonian Cycles in N2-Locally Connected Claw-Free Graphs
30829488
Vertex pancyclism in claw-free graphs
Abstract In this paper, we show four sufficient conditions for vertex pancyclicity in claw-free graphs. These results improve, respectively, results of Broersma and Veldman, Gould and Jacobson, and Ryjacek. In particular, we prove that if G is a 3-connected claw-free graph such that the vertices of degree 1 of every induced bull have a common neighbor in G then every vertex of G is contained in a cycle of all possible lengths except for four and five. We conjecture that almost all pancyclic claw-free graphs with minimum degree at least three are vertex pancyclic.
5906681
Circumferences of 2-Connected Claw-Free Graphs
41518374
Longest cycles in regular 2-connected claw-free graphs
In this paper, we show that every 2-connected, k-regular claw-free graph on n vertices contains a cycle of length at least min 4k?2, n (k?8), and this result is best possible.
4909789
On Pancyclic Claw-Free Graphs
979117
The software architecture of a distributed problem-solving environment
This paper describes the functionality and software architecture of a generic problem-solving environment (PSE) for collaborative computational science and engineering. A PSE is designed to provide transparent access to heterogeneous distributed computing resources, and is intended to enhance research productivity by making it easier to construct, run, and analyze the results of computer simulations. Although implementation details are not discussed in depth, the role of software technologies such as CORBA, Java, and XML is outlined. An XML-based component model is presented. The main features of a Visual Component Composition Environment for software development, and an Intelligent Resource Management System for scheduling components, are described. Some prototype implementations of PSE applications are also presented. Copyright 2000 John Wiley & Sons, Ltd.
8308439
From Gene Trees to Species Trees
This paper studies various algorithmic issues in reconstructing a species tree from gene trees under the duplication and the mutation cost model. This is a fundamental problem in computational molecular biology. Our main results are as follows. 
A linear time algorithm is presented for computing all the losses in duplications associated with the least common ancestor mapping from a gene tree to a species tree. This answers a problem raised recently by Eulenstein, Mirkin, and Vingron [J. Comput. Bio., 5 (1998), pp. 135--148]. The complexity of finding an optimal species tree from gene trees is studied. The problem is proved to be NP-hard for the duplication cost and for the mutation cost. Further, the concept of reconciled trees was introduced by Goodman et al. and formalized by Page for visualizing the relationship between gene and species trees. We show that constructing an optimal reconciled tree for gene trees is also NP-hard. Finally, we consider a general reconstruction problem and show it to be NP-hard even for the well-known nearest neighbor interchange distance. A new and efficiently computable metric is defined based on the duplication cost. We show that the problem of finding an optimal species tree from gene trees is NP-hard under this new metric but it can be approximated within factor 2 in polynomial time. Using this approximation result, we propose a heuristic method for finding a species tree from gene trees with uniquely labeled leaves under the duplication cost. Our experimental tests demonstrate that when the number of species is larger than 15 and gene trees are close to each other, our heuristic method is significantly better than the existing program in Page's GeneTree 1.0 that starts the search from a random tree.
10964754
SETRED: Self-training with Editing
Self-training is a semi-supervised learning algorithm in which a learner keeps on labeling unlabeled examples and retraining itself on an enlarged labeled training set. Since the self-training process may erroneously label some unlabeled examples, sometimes the learned hypothesis does not perform well. In this paper, a new algorithm named Setred is proposed, which utilizes a specific data editing method to identify and remove the mislabeled examples from the self-labeled data. In detail, in each iteration of the self-training process, the local cut edge weight statistic is used to help estimate whether a newly labeled example is reliable or not, and only the reliable self-labeled examples are used to enlarge the labeled training set. Experiments show that the introduction of data editing is beneficial, and the learned hypotheses of Setred outperform those learned by the standard self-training algorithm.
3009418
The hamiltonian index of a graph and its branch-bonds
Let $G$ be an undirected and loopless finite graph that is not a path. The minimum $m$ such that the iterated line graph $L^m(G)$ is hamiltonian is called the hamiltonian index of $G,$ denoted by $h(G).$ A reduction method to determine the hamiltonian index of a graph $G$ with $h(G)\geq 2$ is given here. With it we will establish a sharp lower bound and a sharp upper bound for $h(G)$, respectively, which improves some known results of P.A. Catlin et al. [J. Graph Theory 14 (1990)] and H.-J. Lai [Discrete Mathematics 69 (1988)]. Examples show that $h(G)$ may reach all integers between the lower bound and the upper bound.
15883268
The expected size of Heilbronn's triangles
Heilbronn's triangle problem asks for the least /spl Delta/ such that n points lying in the unit disc necessarily contain a triangle of area at most /spl Delta/. Heilbronn initially conjectured /spl Delta/=O(1/n/sup 2/). As a result of concerted mathematical effort it is currently known that there are positive constants c and C such that c log n/n/sup 2//spl les//spl Delta//spl les/C/n/sup 8/7-/spl epsiv// for every constant /spl epsiv/>0. We resolve Heilbronn's problem in the expected case: If we uniformly at random put n points in the unit disc then (i) the area of the smallest triangle has expectation /spl Theta/(1/n/sup 3/); and (ii) the smallest triangle has area /spl Theta/(1/n/sup 3/) with probability almost one. Our proof uses the incompressibility method based on Kolmogorov complexity.