1259128
Independent sets in triangle-free cubic planar graphs
We prove that every triangle-free planar graph on n vertices with maximum degree three has an independent set with size at least 3/8n. This was suggested and later conjectured by Albertson, Bollobas, and Tucker.
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 $L(e)$.
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.
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.
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.
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.
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).
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.
14857147
An economic analysis of the self commitment of thermal units
Given the load profile of an electricity market and the capabilities of the set of generators supplying power to that market, it is likely that at any given point in time, available supply will exceed demand. If only a subset of generators is required, some method is required to commit and de-commit generators. In the past, system operators have employed a centralized method of unit commitment. Deregulation of the electricity industry throws doubt on the continued suitability of this method due to fairness issues and availability of accurate cost data. This paper examines the performance of decentralized unit commitment, where dispatch of generators is determined by offer curves submitted into a spot market by power producers.
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.