51685
An improved linear edge bound for graph linkages
A graph is said to be k-linked if it has at least 2k vertices and for every sequence S1,...,Sk, t1,...,tk of distinct vertices there exist disjoint paths P1,...,Pk such that the ends of Pi are si and ti. Bollobas and Thomason showed that if a simple graph G on n vertices is 2k-connected and G has at least 11kn edges, then G is k-linked. We give a relatively simple inductive proof of the stronger statement that 8kn edges and 2k-connectivity suffice, and then with more effort improve the edge bound to 5kn.
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.
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.
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.
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 $L(e)$.
3050709
Quality assurance in a student-based agile software engineering process
Agile methodologies have proven to be a popular addition to the software engineering toolbox, promising significant advances in quality for small teams, with developers no longer weighed under by the documentation said to characterise traditional approaches. Yet, in spite of these claims, quality assurance remains a question to which agile methodologies have given only a partially satisfactory answer. This work examines quality assurance practices among student developers working within a lightweight iterative development process. Our focus is upon the linkages between their reported practices and the quality levels observed in the systems delivered. The study has identified a range of approaches to improving quality for small, inexperienced teams, with applications to both the educational and SME environments.
2943319
Thermal unit commitment including optimal AC power flow constraints
The authors propose a new algorithm for unit commitment that employs a Lagrange relaxation technique with a new augmentation of the Lagrangian. The new augmentation involves a duplication of variables that allows relaxation of the coupling between generator time-spanning constraints and system-wide instantaneous constraints. This framework allows the possibility of committing units that are required for the VArs that they can produce, as well as for their real power. Furthermore, although the algorithm is very CPU-intensive, the separation structure of the Lagrangian allows its implementation in parallel computers. Their work builds upon that of Batut and Renaud (1992), as well as that of Baldick (1995).
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 …
6233472
Underlying technical issues in electricity deregulation
This paper reports on the results of an attempt by the Power Systems Engineering Research Center (Pserc) and EPRI to determine the technical tools missing in currently unfolding electric power restructuring scenarios. Needed tools have been divided into the functional categories of generation, transmission and distribution. In each category, there seems to be a common need to interface existing technical tools with the new economic unbundling.
1283266
A guided clothoid spline
Abstract A method is described whereby a G 2 planar curve consisting of clothoid (Cornu spiral) segments, circular arcs and straight line segments is constructed. The curve passes through given points, is expressed parametrically, and has the attractive feature that the arc length and curvature are piecewise linear functions of the parameter. The given points through which the curve passes must be restricted somewhat so that a unique clothoid exists between each pair of points.