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Margit Voigt
Margit Voigt is a German mathematician specializing in graph theory and graph coloring. She is a professor of operations research at the University of Applied Sciences Dresden. Voigt completed her Ph.D. in 1992 at the Technische Universität Ilmenau. Her dissertation, ''Über die chromatische Zahl einer speziellen Klasse unendlicher Graphen'' 'On the chromatic number of a special class of infinite graphs''was jointly supervised by Rainer Bodendiek and Hansjoachim Walther. Her results include the first known planar graph that requires five colors for list coloring, and a counterexample to a related conjecture that list coloring of planar graphs requires at most one more color than graph coloring In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices o ... for the same graphs. References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Coloring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color. Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring problems are often stated and studied as-is. This is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operations Research
Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making. It is considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym. Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlap with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Applied Sciences Dresden
The Hochschule für Technik und Wirtschaft Dresden – University of Applied Sciences (HTW Dresden for short) is a university of applied sciences and, after the Technical University Dresden, the second largest university of the city of Dresden, (Saxony). It offers 36 study programmes in engineering, design, economics and the environment. History The HTW Dresden was founded on 16 July 1992 and was initially divided into 6 subject areas with a total of 15 study programmes. In the following year, the university's offering was expanded to include the Departments of Agriculture / Land Conservation (today: Agriculture / Environment / Chemistry) as well as Design. The latter was renamed the Faculty of Design as part of the implementation of new study programmes in 2018. The same year, the Language Centre and University Sports Department were established and the University Library was opened. As a founding member, the HTW Dresden has been one of the five universities in Germany that are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technische Universität Ilmenau
The Technische Universität Ilmenau (''Ilmenau University of Technology'', TU Ilmenau) is a German public research university located in Ilmenau, Thuringia, central Germany. Founded in 1894, it has five academic departments (faculties) with about 4,900 students. Teaching and research are focused on the fields of technology (including computer science), mathematics and natural sciences, business and media. Introduction Background Research and education at the Technische Universität Ilmenau is focused on engineering with strong links to economics and natural sciences. It is the only university in the federal state of Thüringen with the title " Technische Universität". The university began its life in 1894 as the "Thüringisches Technikum", a private training college. This took on the status of "Hochschule für Elektrotechnik" (HfE) before becoming a "Technische Hochschule" (TH) and in 1992 being accorded the title of "Technische Universität" (TU). Academics TU Ilme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hansjoachim Walther
Hansjoachim Walther (16 December 1939 – 17 January 2005) was a German politician and mathematician. He was leader of the German Social Union, a right-wing party modelled after the Bavarian CSU, during the ''Wende'', serving as their parliamentary leader in the Volkskammer. After German reunification, he was co-opted to the Bundestag and appointed as Minister for Special Affairs. Personal life and death Walther was born in 1939 in Bütow, Farther Pomerania, now Bytów, Poland to Joachim Walther and Erika Dobat, two civil servants. His family fled to Zeitz in 1945. In East Germany, he first completed an apprenticeship as ''Spitzendreher'', a metalworking profession, before studying mathematics at the Dresden University of Technology. Walther achieved a doctorate in 1966. Thereafter until his death, he followed a career as an academic at the Ilmenau University of Technology. Walther, who is the namesake of the Walther graph, died in 2005 of a heart attack during a socce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planar Graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection. Plane graphs can be encoded by combinatorial maps or rotation systems. An equivalence class of topologically equivalent drawings on the sphere, usually with additional assumptions such as the absence of isthmuses, is called a pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Coloring
In graph theory, a branch of mathematics, list coloring is a type of graph coloring where each vertex can be restricted to a list of allowed colors. It was first studied in the 1970s in independent papers by Vizing and by Erdős, Rubin, and Taylor. Definition Given a graph ''G'' and given a set ''L''(''v'') of colors for each vertex ''v'' (called a list), a list coloring is a ''choice function'' that maps every vertex ''v'' to a color in the list ''L''(''v''). As with graph coloring, a list coloring is generally assumed to be proper, meaning no two adjacent vertices receive the same color. A graph is ''k''-choosable (or ''k''-list-colorable) if it has a proper list coloring no matter how one assigns a list of ''k'' colors to each vertex. The choosability (or list colorability or list chromatic number) ch(''G'') of a graph ''G'' is the least number ''k'' such that ''G'' is ''k''-choosable. More generally, for a function ''f'' assigning a positive integer ''f''(''v'') to each v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century German Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius ( AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Women Mathematicians
A woman is an adult female human. Prior to adulthood, a female human is referred to as a girl (a female child or adolescent). The plural ''women'' is sometimes used in certain phrases such as "women's rights" to denote female humans regardless of age. Typically, women inherit a pair of X chromosomes, one from each parent, and are capable of pregnancy and giving birth from puberty until menopause. More generally, sex differentiation of the female fetus is governed by the lack of a present, or functioning, SRY-gene on either one of the respective sex chromosomes. Female anatomy is distinguished from male anatomy by the female reproductive system, which includes the ovaries, fallopian tubes, uterus, vagina, and vulva. A fully developed woman generally has a wider pelvis, broader hips, and larger breasts than an adult man. Women have significantly less facial and other body hair, have a higher body fat composition, and are on average shorter and less muscular than men. Througho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theorists
Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discrete mathematics * Graph of a function *Graph of a relation *Graph paper *Chart, a means of representing data (also called a graph) Computing * Graph (abstract data type), an abstract data type representing relations or connections *graph (Unix), Unix command-line utility *Conceptual graph, a model for knowledge representation and reasoning Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also *Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy (suffix from the Greek for "describe," "write" or "draw") *List of information graphics software This is a list of software to create any kind of information graphics: * either includes the ability t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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