5705388
Three-coloring Klein bottle graphs of girth five
We prove that every graph of girth at least five which admits an embedding in the Klein bottle is 3-colorable. This solves a problem raised by Woodburn, and complements a result of Thomassen who proved the same for projective planar and toroidal graphs.
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.
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.
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.
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.
37344904
Power System Bidding Tournaments for a Deregulated Environment
In this paper we describe certain tools for understanding and operating power systems in a deregulated environment. Many of the current models for this competitive market that employ an independent system operator (ISO) for controlling transmission, ensuring fair access and security, and providing a spot market for power will be studied. This centrally-dispatched power pool also ensures that generation meets demand based on bids submitted daily from independent generators (and from customers offering interruptible loads). Currently, most I S 0 bidding models allow only a single bid per day. In this paper, we present an asynchronous bidding scheme as a possible alternative. In particular, we examine the effects of including a feedback mechanism such that upon receiving generation levels from the ISO, independent generators (IGs) be allowed to modify their bid if they so desire. This competitive or ‘sequential’ bidding process should be allowed to take place each day for a predetermined period of time; in this way, IGs will have a chance to compete and hopefully optimize their profit margins. This paper also discusses the development tools necessary for examining the effects of different bidding processes on the I S 0 model and evaluating their capability of driving the market to an efJicient state of operation.
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.
14742276
Finger tracking for the Digital Desk
One trend in computing environments today is to move towards more 'natural' interaction. Another is to make hardware invisible to the user. Both these ideas converge into ubiquitous computing-the Digital Desk is an example of this idea. In this paper, we concentrate on an input device for the Digital Desk, namely the user's fingertip, which is made to act like a mouse. Tracking such an input device is common to a number of augmented reality environments and involves vision and motion analysis. However, previous attempts have focused more on the vision aspect of tracking general objects than on using the information already known about the user's hand, which is the approach taken in this paper. We adopted the goal of tracking the user's fingertips as fast as possible in real time, so that the system could be compared with other input devices by using models such as Fitts' law. Our system is shown to comply with the law adequately.
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 …