9283488
An end-faithful spanning tree counterexample
We find an infinitely-connected graph in which every spanning tree has a 2-way infinite path. This disproves Halin's well-known `end-faithful spanning tree? conjecture, and also disproves a recent conjecture of ?ira?.
2783736
List Edge-Colorings of Series-Parallel Graphs
It is proved that for every integer $k\ge3$, for every (simple) series-parallel graph $G$ with maximum degree at most $k$, and for every collection $(L(e):e\in E(G))$ of sets, each of size at least $k$, there exists a proper edge-coloring of $G$ such that for every edge $e\in E(G)$, the color of $e$ belongs to $L(e)$.
206570580
Sachs' Linkless Embedding Conjecture
Abstract We prove Sachs′ conjecture that a graph can be embedded in 3-space so that it contains no non-trivial link (in the sense of knot theory) if and only if it contains as a minor none of the seven graphs obtainable from K 6 by Y − Δ and Δ − Y exchanges. We also show the following: (i) A graph admits such a "linkless" embedding if and only if it admits a "panelled" embedding, one such that every circuit of the graph bounds a disc disjoint from the remainder of the graph. This was a conjecture of Bohme. (ii) An embedding is panelled if and only if for every subgraph, its complement in 3-space has free fundamental group. This extends a theorem of Scharlemann and Thompson, who proved it for planar graphs. (iii) If two panelled embeddings of the same graph are "different," that is, are not related by an orientation-preserving homeomorphism of the 3-space, then there is a subgraph which is a subdivision of K 5 or K 3, 3 such that the two induced embeddings of this subgraph are still different.
33726107
A menger-like property of tree-width: The finite case
The notion of tree-width was introduced by Robertson and Symour. A graph has tree-width ≦ w if it admits a tree-decomposition of tree-width ≦ w. We prove here that if G is finite and has tree-width ≦ w then it admits a tree-decomposition of tree-width ≦ w which satisfies a certain Menger-like condition. This result will be used in a future paper on well-quasi-ordering infinite graphs of bounded tree-width.
10511288
Clique Minors in Graphs and Their Complements
A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. Let t?1 be an integer, and let G be a graph on n vertices with no minor isomorphic to Kt+1. Kostochka conjectures that there exists a constant c=c(t) independent of G such that the complement of G has a minor isomorphic to Ks, where s=?12(1+1/t)n?c?. We prove that Kostochka's conjecture is equivalent to the conjecture of Duchet and Meyniel that every graph with no minor isomorphic to Kt+1 has an independent set of size at least n/t. We deduce that Kostochka's conjecture holds for all integers t?5, and that a weaker form with s replaced by s?=?12(1+1/(2t))n?c? holds for all integers t?1.
18561897
Excluding infinite minors
Let ? be an infinite cardinal, and let H be either a complete graph with ? vertices, or a tree in which every vertex has valency ?. What can we say about graphs G which (i) have no minor isomorphic to H, or (ii) contain no subgraph which is a subdivision of H?These four questions are answered for each infinite cardinal ?. In each case we find that there corresponds a necessary and sufficient structural condition (or, in some cases, several equivalent conditions) for G not to contain H in the appropriate way. We survey these results and a number of related theorems.
31409070
Hermite interpolation with a pair of spirals
Abstract The Hermite interpolation problem in the plane considered here is to join two points and to match given unit tangent vectors and signed curvatures at the two points with various G 2 curves consisting of a pair of spirals. The rotation of the tangent vector of the interpolating curve from one point to the other is restricted to being less than π. The necessary and sufficient conditions for the existence of each of the various curves are given.
6336074
Developing Case Studies to Enhance Student Learning
In this paper we describe the cases developed in response to the multifaceted challenges we faced in educating IT professionals in intermediate-level programming. The challenges included: the practical nature of the subject, the level of skill attained, preparing students for the workplace and class size. We implemented Problem-Based Learning (PBL) as the teaching and learning method to meet these challenges by helping first-year university students learn programming while simultaneously developing graduate capabilities. This necessitated redevelopment of the curriculum and the way it was taught. We combined software engineering and information systems approaches in real-world scenarios. The cases were designed to help students come to terms with the human side of information technology through the context and method of teaching and learning as they worked through the cases.
6798576
Locational pricing and scheduling for an integrated energy-reserve market
It is well known that given a network that can become constrained on voltage or real power flows, reserves must also be spatially located in order to handle all credible contingencies. However, to date, there is no credible science-based method for assigning and pricing reserves in this way. Presented in this paper is a new scheduling algorithm incorporating constraints imposed by grid security considerations, which include one base case (intact system) and a list of possible contingencies (line-out, unit-lost, and load-growth) of the system. By following a cost-minimizing co-optimization procedure, both power and reserve are allocated spatially for the combined energy and reserve markets. With the Lagrange multipliers (dual variables) obtained, the scheduling algorithm also reveals the locational shadow prices for the reserve and energy requirements. Unlike other pricing and scheduling methods in use, which are usually ad-hoc and are based on engineering judgment and experience, this proposed formulation is likely to perform better in restructured markets when market power is a potential problem. An illustrative example of a modified IEEE 30-bus system is used to introduce concepts and present results.
12699179
Developing the Software Engineering Team
Teamwork is often considered one of the most important "generic skills" that we can provide to graduates entering the information technology profession. Often though, through the rush of covering important content, we short change our students by giving them limited opportunities to learn how to work effectively in teams. Students also often complain that although they are expected to work in teams on projects, they are never given any advice or guidance on how to work in a team (Hart and Stone, 2002). Or, if they are given guidance, it is often from a business perspective that students find difficult to integrate into their software development practice.In this paper we discuss a course-spanning initiative to help students learn teamwork skills. This initiative starts in first year by emphasising a core set of skills directly related to working in teams. These skills are applied in small software development teams, with close tutor supervision focusing students on teamwork rather than upon individual software development. The theme then continues into second and third year where the growing sophistication of the students' teamwork skills is complemented by increasing their independence and requiring students to apply a professional software engineering process as a development team. By the end of their course students are then in a position to work together effectively solving complex problems for a real industry client.
2733176
The pervasiveness of evolution in GRUMPS software
This paper describes the evolution of the design and implementation of a distributed run-time system that itself is designed to support the evolution of the topology and implementation of an executing, distributed system. The three different versions of the run-time architecture that have been designed and implemented are presented, together with how each architecture addresses the problems of topological and functional evolution. In addition, the reasons for the rapid evolution of the design and implementation of the architecture are also described.From the lessons learned in both evolving the design of the architecture and in trying to provide a run-time system that can support run-time evolution, this paper discusses two generally applicable observations: evolution happens all the time, and it is not possible to anticipate how systems will evolve as designs; and large, run-time systems do not follow a predictable path. In addition to this, rapid prototyping has proved to be extremely useful in the production of the three architectures; this kind of prototyping has been made much easier by designing the core set of Java abstractions in terms of interfaces; and building an architecture that allows as many decisions as possible to be made at run-time which has produced a support system that is more responsive to the user as well as the distributed environment in which it is executing.