5196479
Odd Wheels in Graphs
For k?1 the odd wheel of 2k+1 spokes, denoted by W2k+1, is the graph obtained from a cycle of length 2k+1 by adding a new vertex and joining it to all vertices of the cycle. In this paper it is shown that if a graph G of order n with minimum degree greater than 7n/12 is at least 4-chromatic then G contains an odd wheel with at most 5 spokes.
3399031
On 2-factors in claw-free graphs
Abstract A graph is said claw-free if it contains no induced subgraph isomorphic to K 1,3 . We prove that if G is a claw-free graph with minimum degree δ ⩾4, then G contains a 2-factor with at most 6 n /( δ +2)−1 components. Moreover, together with a theorem of Choudoum and Paulraj (J. Graph Theory 15 (1991) 259–265) and one of Anstee (J. Algorithms 6 (1985) 112–131), it is polynomial (in O( n 3 )) to construct such a 2-factor.
38894685
A Strongly Polynomial Algorithm for the Inverse Shortest Arborescence Problem
Abstract In this paper an inverse problem of the weighted shortest arborescence problem is discussed. That is, given a directed graph G and a set of nonnegative costs on its arcs, we need to modify those costs as little as possible to ensure that T, a given v1 -arborescence of G, is the shortest one. It is found that only the cost of T needs modifying. An O(n3) combinatorial algorithm is then proposed. This algorithm also gives an optimal solution to the inverse weighted shortest path problem.
42940477
Hamiltonian iterated line graphs
The n-iterated line graph of a graph G is Ln(G) = L(Ln-1(G)), where L1(G) denotes the line graph L(G) of G, and Ln-1(G) is assumed to be nonempty. Harary and Nash-Williams characterized those graphs G for which L(G) is hamiltonian. In this paper, we will give a characterization of those graphs G for which Ln(G) is hamiltonian, for each n ≥ 2. This is not a simple consequence of Harary and Nash-Williams' result. As an application, we show two methods for determining the hamiltonian index of a graph and enhance various results on the hamiltonian index known earlier.
7550543
A digital library for geography examination resources
We describe a Web-based application developed above a digital library of geographical resources for Singapore students preparing to take a national examination in geography. The application provides an interactive, non-sequential approach to learning that supplements textbooks.
8080684
Well-Behaved Inference Rules for First-Order Theorem Proving
The concept of well-behaved inference rules is developed in first-order polynomial-based theorem proving. It is shown that well-behaved inference rules are complete for both the set of support strategy and the linear strategy. Furthermore, two concrete inference rules that are well behaved are presented, and two other strategies for them are described.
11497838
On organizing and accessing geospatial and georeferenced Web resources using the G-Portal system
In order to organise and manage geospatial and georeferenced information on the Web making them convenient for searching and browsing, a digital portal known as G-Portal has been designed and implemented. Compared to other digital libraries, G-Portal is unique for several of its features. It maintains metadata resources in XML with flexible resource schemas. Logical groupings of metadata resources as projects and layers are possible to allow the entire metadata collection to be partitioned differently for users with different information needs. These metadata resources can be displayed in both the classification-based and map-based interfaces provided by G-Portal. G-Portal further incorporates both a query module and an annotation module for users to search metadata and to create additional knowledge for sharing respectively. G-Portal also includes a resource classification module that categorizes resources into one or more hierarchical category trees based on user-defined classification schemas. This paper gives an overview of the G-Portal design and implementation. The portal features will be illustrated using a collection of high school geography examination-related resources.
16029762
Preemptive Scheduling with Variable Profile, Precedence Constraints and Due Dates
Abstract This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an earliest due date first algorithm provides an optimal nonpreemptive schedule for unit-execution-time (UET) tasks, the preemptive priority scheduling algorithm, referred to as smallest laxity first, provides an optimal preemptive schedule for real-execution-time (RET) tasks. When the objective is to minimize the makespan, we get the same kind of result between highest level first schedules solving nonpreemptive tasks with UET and the longest remaining path first schedule for the corresponding preemptive scheduling problem with RET tasks. These results are applied to four specific profile scheduling problems and new optimality results are obtained.
9905546
Mean eccentricities of de Bruijn networks
Given a graph G = (V; E) we deene e(X), the mean eccentricity of a vertex X, as the average distance from X to all the other vertices of the graph. The computation of this parameter appears to be nontrivial in the case of the de Bruijn networks. In this paper we consider upper and lower bounds for e(X). For the directed de Bruijn network, we provide tight bounds as well as the extremal vertices which reach these bounds. These bounds are expressed as the diameter minus some constants. In the case of undirected networks, the computation turns out to be more diicult. We provide lower and upper bounds which diier from the diameter by some small constants. We conjecture that the vertices of the form a a have the largest mean eccentricity. Numerical computations indicate that the conjecture holds for binary de Bruijn networks with diameters up to 18. We prove that the asymptotic diierence, when the diameter goes to innnity, between the mean eccentricities of an arbitrary vertex and that of a a is smaller than a small constant tending to zero with the degree. We also provide a simple recursive scheme for the computation of the asymptotic mean eccentricity of the vertices a a. A by-product of our analysis is that in both directed and undirected de Bruijn networks, most of the vertices are at distance near from the diameter and that all of the mean eccentricities tend to the diameter when the degree goes to innnity.