31462634
Kuratowski Chains
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.
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.
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 $L(e)$.
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.
17884360
Experimental results for single period auctions
The objective of the paper is to present experimental results for testing the performance of different auction mechanisms related to the introduction of competitive markets for the generation of electricity. The research is based on the concept of smart markets introduced by Vernon Smith (K.A. McCabe et al., 1991) and a simulation model (PowerWeb) of a realistic bulk power system. There are unique physical aspects associated with the supply of electricity (e.g. required instantaneous matching of supply and demand, unintended congestion of parallel transmission routes and maintenance of system stability in response to disturbances). As a result, traditional theories of efficient markets and auction structures developed for other commodities may not be efficient if applied without alteration to markets for electricity. Conversely, current utility rules of operation developed for a centrally planned regime may not be appropriate in a competitive environment. The research does not address the issues of multiperiod operations (unit commitment) and multidimensional markets (ancillary services), and considers only real power in a single time period. The main objective is to test three alternative auction mechanisms when market power is a potential problem. This situation occurs when limits on transmission lines are binding to form a load pocket in which demand is met by a few (in this case two) generators.
33773
An Agent-Based Optimal Bidding Function
Problems such as price volatility have been observed in electric power markets. Demand-side participation is often offered as a potential solution by promising to increase market efficiency when hockey-stick type offer curves are present. However, individual end-consumer will surely value electricity differently, which makes demand-side participation as a group and at a bus difficult. In this paper demand is categorized into two groups: one that highly values reliability and the other that does not. The two types are modeled separately and a new optimal bidding function is developed and tested based on this model.
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.
10283778
An Internet-based platform for testing generation scheduling auctions
The paper describes the uses and architecture of a network-centered computing-rich software platform called PowerWeb. PowerWeb was designed and built as a simulation environment for experimentally testing various power exchange auction markets through tournaments. It is designed to host simulations of a competitive "day-ahead" electric energy market in the content of a restructured electric power industry. The PowerWeb environment is meant to be flexible so as to accommodate different "rules of the game". The authors describe its interactive, distributed and Web-based character.
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 …