31141074
Petersen Family Minors
Abstract We show that the only graphs with certain connectivity and planarity properties are the Petersen graph and some other more trivial graphs. Then this is used to show that every graph with no minor in the Petersen family (the seven graphs that can be obtained from the Petersen graph by Y − Δ and Δ − Y exchanges) is either decomposable in some sense, or it is a 1-vertex extension of a planar graph, or it has high connectivity in a sense we can use, or it can be converted to one of these by Y − Δ and Δ − Y exchanges. This is a lemma for use in a subsequent paper, where we show that a graph has a "linkless" embedding in 3-space if and only if it has no minor in the Petersen family.
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.
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 $L(e)$.
206570506
Quickly Excluding a Planar Graph
Abstract In an earlier paper, the first two authors proved that for any planar graph H , every graph with no minor isomorphic to H has bounded tree width; but the bound given there was enormous. Here we prove a much better bound. We also improve the best known bound on the tree-width of planar graphs with no minor isomorphic to a g × g grid.
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.
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.
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).
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.
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.
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.