List precoloring extension in planar graphs

A celebrated result of Thomassen states that not only can every planar graph be colored properly with five colors, but no matter how arbitrary palettes of five colors are assigned to vertices, one can choose a color from the corresponding palette for each vertex so that the resulting coloring is proper. This result is referred to as 5-choosability of planar graphs. Albertson asked whether Thomassen's theorem can be extended by precoloring some vertices which are at a large enough distance apart in a graph. Here, among others, we answer the question in the case when the graph does not contain short cycles separating precolored vertices and when there is a "wide" Steiner tree containing all the precolored vertices.Comment: v2: 15 pages, 11 figres, corrected typos and new proof of Theorem 3(2

Introduction: Analytic, Continental and the question of a bridge

This is the peer reviewed version of the following article: Introduction: Analytic, Continental and the question of a bridge, which has been published in final form at 10.1177/1474885115582078. This article may be used for non-commercial purposes in accordance with SAGE’s Terms and Conditions for Self-Archiving.In philosophy and political theory, divisions come and go, but some persist despite beingobviously problematic. The analytic and Continental divide is one such division. Inpolitical philosophy and political theory, the division has been particularly pronounced.Analytic and Continental thinkers are divided not only over substantial issues but also over the very nature of political theorising. In spite of this fundamental nature, theorists often seem to assume that, as a division, the analytic/Continental divide requires no explanation. We suggest that, as a central division within political theory, and despite being acknowledged as problematic for quite some time, it has persisted because it has not been adequately examined. Once examined, the division turns out to be operationally weaker than it once was. In recent years, there has been a growing interest in engaging thinkers from the other side. This has been accompanied by a corresponding tendency, among both analytic and Continental philosophers and political thinkers, to reflect on the nature of their own tradition and ‘philosophy’. Both traditions have entered a self-conscious period of meta-reflection. Such questioning indicates the possibility of transformation within both groups, in the absence of settled frameworks and divisions. However, it is also clear that such signs are the beginning of the possibility of a new relation rather than a sign of the eclipse of the division. The continued institutional separation and the space between their respective philosophical vocabularies suggest that, while the time is ripe for work here, there is still much to be done

Morphing Planar Graph Drawings Optimally

We provide an algorithm for computing a planar morph between any two planar straight-line drawings of any $n$-vertex plane graph in $O(n)$ morphing steps, thus improving upon the previously best known $O(n^2)$ upper bound. Further, we prove that our algorithm is optimal, that is, we show that there exist two planar straight-line drawings $\Gamma_s$ and $\Gamma_t$ of an $n$-vertex plane graph $G$ such that any planar morph between $\Gamma_s$ and $\Gamma_t$ requires $\Omega(n)$ morphing steps

Introduction to the Special Issue on Liminal Hotspots

This article introduces a special issue of Theory and Psychology on liminal hotspots. A liminal hotspot is an occasion during which people feel they are caught suspended in the circumstances of a transition that has become permanent. The liminal experiences of ambiguity and uncertainty that are typically at play in transitional circumstances acquire an enduring quality that can be described as a “hotspot”. Liminal hotspots are characterized by dynamics of paradox, paralysis, and polarization, but they also intensify the potential for pattern shift. The origins of the concept are described followed by an overview of the contributions to this special issue

Pole Dancing: 3D Morphs for Tree Drawings

We study the question whether a crossing-free 3D morph between two straight-line drawings of an $n$-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the two given drawings are two-dimensional and at the one in which they are three-dimensional. In the former setting we prove that a crossing-free 3D morph always exists with $O(\log n)$ steps, while for the latter $\Theta(n)$ steps are always sufficient and sometimes necessary.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Straight-line Drawability of a Planar Graph Plus an Edge

We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line drawing, and a linear-time drawing algorithm that constructs such a drawing, if it exists. We also show that some almost-planar graphs require exponential area for a straight-line drawing

Some Results On Convex Greedy Embedding Conjecture for 3-Connected Planar Graphs

A greedy embedding of a graph $G = (V,E)$ into a metric space $(X,d)$ is a function $x : V(G) \to X$ such that in the embedding for every pair of non-adjacent vertices $x(s), x(t)$ there exists another vertex $x(u)$ adjacent to $x(s)$ which is closer to $x(t)$ than $x(s)$. This notion of greedy embedding was defined by Papadimitriou and Ratajczak (Theor. Comput. Sci. 2005), where authors conjectured that every 3-connected planar graph has a greedy embedding (possibly planar and convex) in the Euclidean plane. Recently, greedy embedding conjecture has been proved by Leighton and Moitra (FOCS 2008). However, their algorithm do not result in a drawing that is planar and convex for all 3-connected planar graph in the Euclidean plane. In this work we consider the planar convex greedy embedding conjecture and make some progress. We derive a new characterization of planar convex greedy embedding that given a 3-connected planar graph $G = (V,E)$, an embedding x: V \to \bbbr^2 of $G$ is a planar convex greedy embedding if and only if, in the embedding $x$, weight of the maximum weight spanning tree ($T$) and weight of the minimum weight spanning tree (\func{MST}) satisfies \WT(T)/\WT(\func{MST}) \leq (\card{V}-1)^{1 - \delta}, for some $0 < \delta \leq 1$.Comment: 19 pages, A short version of this paper has been accepted for presentation in FCT 2009 - 17th International Symposium on Fundamentals of Computation Theor

On vertex coloring without monochromatic triangles

We study a certain relaxation of the classic vertex coloring problem, namely, a coloring of vertices of undirected, simple graphs, such that there are no monochromatic triangles. We give the first classification of the problem in terms of classic and parametrized algorithms. Several computational complexity results are also presented, which improve on the previous results found in the literature. We propose the new structural parameter for undirected, simple graphs -- the triangle-free chromatic number $\chi_3$. We bound $\chi_3$ by other known structural parameters. We also present two classes of graphs with interesting coloring properties, that play pivotal role in proving useful observation about our problem. We give/ask several conjectures/questions throughout this paper to encourage new research in the area of graph coloring.Comment: Extended abstrac

Placing regenerators in optical networks to satisfy multiple sets of requests.

The placement of regenerators in optical networks has become an active area of research during the last years. Given a set of lightpaths in a network G and a positive integer d, regenerators must be placed in such a way that in any lightpath there are no more than d hops without meeting a regenerator. While most of the research has focused on heuristics and simulations, the first theoretical study of the problem has been recently provided in [10], where the considered cost function is the number of locations in the network hosting regenerators. Nevertheless, in many situations a more accurate estimation of the real cost of the network is given by the total number of regenerators placed at the nodes, and this is the cost function we consider. Furthermore, in our model we assume that we are given a finite set of p possible traffic patterns (each given by a set of lightpaths), and our objective is to place the minimum number of regenerators at the nodes so that each of the traffic patterns is satisfied. While this problem can be easily solved when d = 1 or p = 1, we prove that for any fixed d,p ≥ 2 it does not admit a PTASUnknown control sequence '\textsc', even if G has maximum degree at most 3 and the lightpaths have length O(d)(d). We complement this hardness result with a constant-factor approximation algorithm with ratio ln (d ·p). We then study the case where G is a path, proving that the problem is NP-hard for any d,p ≥ 2, even if there are two edges of the path such that any lightpath uses at least one of them. Interestingly, we show that the problem is polynomial-time solvable in paths when all the lightpaths share the first edge of the path, as well as when the number of lightpaths sharing an edge is bounded. Finally, we generalize our model in two natural directions, which allows us to capture the model of [10] as a particular case, and we settle some questions that were left open in [10]

Ergonomics in control room design

Ergonomic contributions in early design phases of large-scale projects are not yet common practice. In this paper a description is given of a control room design project, in which ergonomists participated from the very beginning. First, the scope of the project and a methodical approach to the design are introduced. This is followed by an overview of the activities of ergonomists in this particular project. The second part of this paper concerns the experiences with this methodical approach and design practice. These are discussed by the former control room project manager, one of the ergonomists, the interior architect and a user representative. It is concluded that it is possible to include ergonomics as well as user participation in every design phase without getting behind on time schedules and keeping within available budgets. A lot of useful design and engineering data could be derived from the situation analysis in the existing situation and the full-scale mock-up evaluation that was carried out. Besides workplace design, job design (operator workload) and work organization design were essential to the success of the project