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Bruce Reed (mathematician)
Bruce Alan Reed FRSC is a Canadian mathematician and computer scientist, a former Canada Research Chair in Graph Theory at McGill University. His research is primarily in graph theory.Chairholders: Bruce A. Reed Canada Research Chairs, retrieved 2012-10-07. He is a distinguished research fellow of the Institute of Mathematics in the , Taiwan, and an adjunct professor at the in Canada. Academic career Reed earned his P ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bruce Reed, Bellairs 2015
The English language name Bruce arrived in Scotland with the Normans, from the place name Brix, Manche in Normandy, France, meaning "the willowlands". Initially promulgated via the descendants of king Robert the Bruce (1274−1329), it has been a Scottish surname since medieval times; it is now a common given name. The variant ''Lebrix'' and ''Le Brix'' are French variations of the surname. Actors * Bruce Bennett (1906–2007), American actor and athlete * Bruce Boxleitner (born 1950), American actor * Bruce Campbell (born 1958), American actor, director, writer, producer and author * Bruce Davison (born 1946), American actor and director * Bruce Dern (born 1936), American actor * Bruce Gray (1936–2017), American-Canadian actor * Bruce Greenwood (born 1956), Canadian actor and musician * Bruce Herbelin-Earle (born 1998), English-French actor and model * Bruce Jones (born 1953), English actor * Bruce Kirby (1925–2021), American actor * Bruce Lee (1940–1973), martial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Method
The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is strictly greater than zero. Although the proof uses probability, the final conclusion is determined for ''certain'', without any possible error. This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding), and information theory. Introduction If every object in a collection of objects fails to have a certain property, then the probability that a random object chosen from the collection has that property is zero. Similarly, showing that the probability is (strictly) less than 1 can be used to prove the existence of an object that does ''not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics, Probability And Computing
''Combinatorics, Probability and Computing'' is a peer-reviewed scientific journal in mathematics published by Cambridge University Press. Its editor-in-chief is Béla Bollobás (DPMMS and University of Memphis). History The journal was established by Bollobás in 1992. Fields Medalist Timothy Gowers calls it "a personal favourite" among combinatorics journals and writes that it "maintains a high standard". Content The journal covers combinatorics, probability theory, and theoretical computer science. Currently, it publishes six issues annually. As with other journals from the same publisher, it follows a hybrid green/gold open access policy, in which authors may either place copies of their papers in an institutional repository after a six-month embargo period, or pay an open access charge to make their papers free to read on the journal's website. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the jou ... [...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] |
Chromatic Number
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] |
Benny Sudakov
Benny Sudakov (born October 1969) is an Israeli mathematician, who works mainly on Hungarian-style combinatorics. He was born in Tbilissi, Georgia, and completed his undergraduate studies at Tbilisi State University in 1990. After emigrating to Israel, he received his Doctor of Philosophy, PhD from Tel Aviv University in 1999, under the supervision of Noga Alon. From 1999 until 2002 he held a Veblen Research Instructorship, a joint position between Princeton University and the Institute for Advanced Study. Until 2007 he was an assistant professor at Princeton University. Until 2014, he was a professor at the University of California, Los Angeles. In July 2013 Sudakov joined ETH Zurich as a professor. Sudakov has broad interests within the field of combinatorics, having written papers on extremal combinatorics, Ramsey theory, random graphs, and positional games. In 2012 he became a Fellow of the American Mathematical Society. He gave an list of International Congresses of Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Mathematical Union
The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports the International Congress of Mathematicians. Its members are national mathematics organizations from more than 80 countries. The objectives of the International Mathematical Union (IMU) are: promoting international cooperation in mathematics, supporting and assisting the International Congress of Mathematicians (ICM) and other international scientific meetings/conferences, acknowledging outstanding research contributions to mathematics through the awarding of scientific prizes, and encouraging and supporting other international mathematical activities, considered likely to contribute to the development of mathematical science in any of its aspects, whether pure, applied, or educational. The IMU was established in 1920, but dissolved in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of International Congresses Of Mathematicians Plenary And Invited Speakers
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." The current list of Plenary and Invited Speakers presented here is based on the ICM's post-WW II terminology, in which the one-hour speakers in the morning sessions are called "Plenary Speakers" and the other speakers (in the afternoon sessions) whose talks are included in the ICM published proceedings are called "Invited Speakers". In the pre-WW II congresses the Plenary Speakers were called "Invited Speakers". By congress year 1897, Zürich * Jules Andrade * Léon Autonne *Émile Borel * N. V. Bougaïev *Francesco Brioschi *Hermann Brunn *Cesare Burali-Forti *Charles Jean de la Vallée Poussin *Gustaf Eneström *Federigo Enriques *Gino Fano * Zoel García de Galdeano * Francesco Gerbaldi *Paul Gordan *Jacques Hadamard * Adolf Hurwitz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lovász Local Lemma
In probability theory, if a large number of events are all independent of one another and each has probability less than 1, then there is a positive (possibly small) probability that none of the events will occur. The Lovász local lemma allows one to relax the independence condition slightly: As long as the events are "mostly" independent from one another and aren't individually too likely, then there will still be a positive probability that none of them occurs. It is most commonly used in the probabilistic method, in particular to give existence proofs. There are several different versions of the lemma. The simplest and most frequently used is the symmetric version given below. A weaker version was proved in 1975 by László Lovász and Paul Erdős in the article ''Problems and results on 3-chromatic hypergraphs and some related questions''. For other versions, see . In 2020, Robin Moser and Gábor Tardos received the Gödel Prize for their algorithmic version of the Lovász L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree Decomposition
In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph. Tree decompositions are also called junction trees, clique trees, or join trees. They play an important role in problems like probabilistic inference, constraint satisfaction, query optimization, and matrix decomposition. The concept of tree decomposition was originally introduced by . Later it was rediscovered by and has since been studied by many other authors. Definition Intuitively, a tree decomposition represents the vertices of a given graph as subtrees of a tree, in such a way that vertices in are adjacent only when the corresponding subtrees intersect. Thus, forms a subgraph of the intersection graph of the subtrees. The full intersection graph is a chordal graph. Each subtree associates a graph vertex with a set of tree nodes. To define this formally, we represent each t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acyclic Coloring
In graph theory, an acyclic coloring is a (proper) Graph coloring, vertex coloring in which every 2-chromatic subgraph is Glossary of graph theory, acyclic. The acyclic chromatic number of a Graph (discrete mathematics), graph is the fewest colors needed in any acyclic coloring of . Acyclic coloring is often associated with graphs Graph embedding, embedded on non-plane surfaces. Upper bounds A(''G'') ≤ 2 if and only if ''G'' is acyclic. Bounds on A(''G'') in terms of Δ(''G''), the Glossary of graph theory, maximum degree of ''G'', include the following: * A(''G'') ≤ 4 if Δ(''G'') = 3. * A(''G'') ≤ 5 if Δ(''G'') = 4. * A(''G'') ≤ 7 if Δ(''G'') = 5. * A(''G'') ≤ 12 if Δ(''G'') = 6. A milestone in the study of acyclic coloring is the following affirmative answer to a conjecture of Grünbaum: :Theorem A(''G'') ≤ 5 if ''G'' is planar graph. introduced acyclic coloring and acyclic chromatic number, and conjectured the result in the above theorem. Borodin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Satisfiability Problem
In mathematical logic, a formula is ''satisfiable'' if it is true under some assignment of values to its variables. For example, the formula x+3=y is satisfiable because it is true when x=3 and y=6, while the formula x+1=x is not satisfiable over the integers. The dual concept to satisfiability is validity; a formula is ''valid'' if every assignment of values to its variables makes the formula true. For example, x+3=3+x is valid over the integers, but x+3=y is not. Formally, satisfiability is studied with respect to a fixed logic defining the syntax of allowed symbols, such as first-order logic, second-order logic or propositional logic. Rather than being syntactic, however, satisfiability is a semantic property because it relates to the ''meaning'' of the symbols, for example, the meaning of + in a formula such as x+1=x. Formally, we define an interpretation (or model) to be an assignment of values to the variables and an assignment of meaning to all other non-logical symbols, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
