6227339
Proper minor-closed families are small
We prove that for every proper minor-closed class I of graphs there exists a constant c such that for every integer n the class I includes at most n!cn graphs with vertex-set {1, 2,...,n}. This answers a question of Welsh.
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.
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.
21521950
A new proof of the independence ratio of triangle-free cubic graphs
Abstract Staton proved that every triangle-free graph on n vertices with maximum degree 3 has an independent set of size at least 5 n /14. A simpler proof was found by Jones. We give a yet simpler proof, and use it to design a linear-time algorithm to find such an independent set.
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.
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.
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.
16046081
A method for classifying offer strategies observed in an electricity market
The idea that large-scale generating units will operate at marginal cost when given the ability to offer their power for sale in a uniform price auction is at best wishful thinking. In fact, both real and experimental data show that the more uncertainty a supplier faces (e.g., load uncertainty, uncertainty of other suppliers, etc.), the more they will hedge their profits through higher than marginal cost offers and through withholding units if permitted. This makes predicting unit commitment and dispatch ahead of time difficult. This paper explores characteristics of software agents that were designed based on the outcome of human subject experiments on a uniform price auction with stochastic load. The agent behavior is compared to the behavior of the subjects. Both subject and agent behavior is classified based on the data. Differences and similarities are noted and explained. Based on the result of the simulation, a model was suggested to explain an offer submitted in deregulated markets based on double layer diffusion.
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.
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.