1707475
Excluding a Countable Clique
We extend the excludedKnminor theorem of Robertson and Seymour to infinite graphs and deduce a structural characterization of the infinite graphs that have noK?0minor. The latter is a refinement of an earlier characterization of Robertson, Seymour, and the second author.
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.
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.
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.
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.
13961083
Experimental tests of competitive markets for electric power
Testing the performance of electricity markets using POWERWEB has already shown that relatively inexperienced players can identify and exploit market power in load pockets. When transmission constraints are not binding, however, auctions with six players have been shown to be efficient. There is evidence from operating electricity markets that prices can be driven above competitive levels when the largest supplier controls less than 20% of total installed capacity. This is accomplished by causing price spikes to occur. In experiments, uncertainty about the actual load and paying standby costs regardless of whether or not a unit is actually dispatched contribute to volatile price behavior. The objective of this paper is to investigate characteristics of a market that affect price volatility. The tests consider three different sets of rules for setting price when there are capacity shortfalls, and the following four market structures: load is responsive to price; price forecasts are made before market settlement; a day-ahead market and a balancing market auction; and suppliers are paid actual offers (a discriminatory auction).
2021116
Industry experience in migrating to object technology
Object oriented software engineering (OOSE) is becoming a common approach to software development. As third generation OOSE processes are established (e.g. OPEN (I. Graham, 1997) and the Unified Software Development Process (I. Jacobson, 1999)) organisations will start to consider OOSE as a mature technology. This recognition will mean that more organisations will go through the process of changing their current software development processes. The paper reports on the experience of one team at a large technical firm as they adopted OOSE processes for a major project. The experience of this team confirms most of what has been previously reported in the literature, and adds two additional observations. The first observation is that other literature in this field does not consider team motivation as a factor that contributes to migration success. The second observation is that other literature does not consider the relative impact of some factors over other factors.
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.
12496489
Studying long-term system use
here have been many studies of computer users but few that extend over very long periods. The reasons for this include costs, the quality of the data that can be obtained and satisfactorily analyzed , and the requirement to obtain results in the short term. We were interested in building long-term user models for teaching systems and wished to track the total development of a guru as well as other types of users. Such goals require tracking large numbers of people over a very long period, because guru-level experience takes years to acquire, and it cannot be predicted in advance who will turn out to develop this level of skill. Therefore, to find even one guru may require the tracking of around 20 to 100 users for a year or two. Finding 10 gurus might require 1,000 users. It is possible to observe such numbers over years only by using a method that is very careful about costs. The objective of this article is to present a methodology for monitoring many users in their natural settings over the long term and to give an example of its application to the domain of students learning an editor for three years. We show how data obtained from this methodology permits the construction of individual user models. Monitoring Methodology We developed a monitoring system to study the use of the sam text editor [13]. It is essentially a modeless editor, with most basic commands invoked using the mouse. It also has powerful keyboard commands, issued through the command window, including the usual Unix regular expressions and an elegant interface to the Unix shell. We had a number of design goals for our system, which strongly influenced our methods. First, we were restricted to low system-building costs followed by very low operational costs. Second, the system needed to be highly reliable; it would not be possible to make changes once the monitoring was under way, nor could the immediate availability of people to fix problems during operation be guaranteed. Third, the impact on the computing resources had to be negligible-a degradation in performance during the day was not an option. Fourth, we wanted to give the users some control over their own data, they should be able to read it and delete it if they really wanted. Finally, and most demandingly, we wanted to measure the time of first use of each command, but …
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.