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Vadim G. Vizing
Vadim Georgievich Vizing (russian: Вади́м Гео́ргиевич Визинг, uk, Вадим Георгійович Візінг; 25 March 1937 – 23 August 2017) was a Soviet and Ukrainian mathematician known for his contributions to graph theory, and especially for Vizing's theorem stating that the edges of any simple graph with maximum degree Δ can be colored with at most Δ + 1 colors. Biography Vizing was born in Kiev on March 25, 1937. His mother was half-German,"Vizing" may be the romanization of the phonetic transcription of the German surname Wiesing into Russian. and because of this the Soviet authorities forced his family to move to Siberia in 1947. After completing his undergraduate studies in mathematics in Tomsk State University in 1959, he began his Ph.D. studies at the Steklov Institute of Mathematics in Moscow, on the subject of function approximation, but he left in 1962 without completing his degree. Instead, he returned to Novosibir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
USSR
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national republics; in practice, both its government and its economy were highly centralized until its final years. It was a one-party state governed by the Communist Party of the Soviet Union, with the city of Moscow serving as its capital as well as that of its largest and most populous republic: the Russian SFSR. Other major cities included Leningrad (Russian SFSR), Kiev ( Ukrainian SSR), Minsk ( Byelorussian SSR), Tashkent (Uzbek SSR), Alma-Ata (Kazakh SSR), and Novosibirsk (Russian SFSR). It was the largest country in the world, covering over and spanning eleven time zones. The country's roots lay in the October Revolution of 1917, when the Bolsheviks, under the leadership of Vladimir Lenin, overthrew the Russian Provisional Gove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American people, American mathematician, electrical engineering, electrical engineer, and cryptography, cryptographer known as a "father of information theory". As a 21-year-old master's degree student at the Massachusetts Institute of Technology (MIT), he wrote A Symbolic Analysis of Relay and Switching Circuits, his thesis demonstrating that electrical applications of Boolean algebra could construct any logical numerical relationship. Shannon contributed to the field of cryptanalysis for national defense of the United States during World War II, including his fundamental work on codebreaking and secure telecommunications. Biography Childhood The Shannon family lived in Gaylord, Michigan, and Claude was born in a hospital in nearby Petoskey, Michigan, Petoskey. His father, Claude Sr. (1862–1934), was a businessman and for a while, a judge of probate in Gaylord. His mother, Mabel Wolf Shannon (1890–1945), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1937 Births
Events January * January 1 – Anastasio Somoza García becomes President of Nicaragua. * January 5 – Water levels begin to rise in the Ohio River in the United States, leading to the Ohio River flood of 1937, which continues into February, leaving 1 million people homeless and 385 people dead. * January 15 – Spanish Civil War: Second Battle of the Corunna Road ends inconclusively. * January 20 – Second inauguration of Franklin D. Roosevelt: Franklin D. Roosevelt is sworn in for a second term as President of the United States. This is the first time that the United States presidential inauguration occurs on this date; the change is due to the ratification in 1933 of the Twentieth Amendment to the United States Constitution. * January 23 – Moscow Trials: Trial of the Anti-Soviet Trotskyist Center – In the Soviet Union 17 leading Communists go on trial, accused of participating in a plot led by Leon Trotsky to overthrow Joseph Stalin's regime, and assas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sobolev Institute Of Mathematics
The Sobolev Institute of Mathematics (SIM) was founded in 1957 by Sergey Sobolev. It is located in Akademgorodok and it constitutes part of the Siberian Branch of the Russian Academy of Sciences. Sergey S. Goncharov is the director. The institute was founded as part of a broader project developed by Sobolev, Mikhail Lavrentyev and Sergey Khristianovich which received official support on 18 May 1957. The broader project led to the foundation of the Novosibirsk State University and the town of Akademgorodok. However SIM was one of the first academic institutes to be set up being founded in 1957. Journals * ''Algebra and logic'' Editor: Yuri L. Ershov * ''Siberian Mathematical Journal'' Editor-in-Chief: Yuri L. Ershov * ''Siberian Advances in Mathematics'' Editor-in-Chief: Alexander A. Borovkov * ''Matematicheskie Trudy'' (Mathematical Proceedings) Editor-in-chief: Alexander A. Borovkov * ''Journal of Applied and Industrial Mathematics'' Editor-in-Chief: Vladimir G. Romanov *Siberian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Job Shop Scheduling
Job-shop scheduling, the job-shop problem (JSP) or job-shop scheduling problem (JSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job scheduling problem, we are given ''n'' jobs ''J''1, ''J''2, ..., ''Jn'' of varying processing times, which need to be scheduled on ''m'' machines with varying processing power, while trying to minimize the makespan – the total length of the schedule (that is, when all the jobs have finished processing). In the specific variant known as ''job-shop scheduling'', each job consists of a set of ''operations'' ''O''1, ''O''2, ..., ''On'' which need to be processed in a specific order (known as ''precedence constraints''). Each operation has a ''specific machine'' that it needs to be processed on and only one operation in a job can be processed at a given time. A common relaxation is the flexible job shop, where each operation can be processed on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brooks' Theorem
In graph theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a connected graph in which every vertex has at most Δ neighbors, the vertices can be colored with only Δ colors, except for two cases, complete graphs and cycle graphs of odd length, which require Δ + 1 colors. The theorem is named after R. Leonard Brooks, who published a proof of it in 1941. A coloring with the number of colors described by Brooks' theorem is sometimes called a ''Brooks coloring'' or a Δ-''coloring''. Formal statement For any connected undirected graph ''G'' with maximum degree Δ, the chromatic number of ''G'' is at most Δ, unless ''G'' is a complete graph or an odd cycle, in which case the chromatic number is Δ + 1. Proof gives a simplified proof of Brooks' theorem. If the graph is not biconnected, its biconnected components may be colored separately and then the colorings combined. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Clique
In the mathematical area of graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. That is, a clique of a graph G is an induced subgraph of G that is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied. Although the study of complete subgraphs goes back at least to the graph-theoretic reformulation of Ramsey theory by , the term ''clique'' comes from , who used complete subgraphs in social networks to model cliques of people; that is, groups of people all of whom know each other. Cliques have many other applications in the sciences and particularly in bioinf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subgraph Isomorphism
In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs ''G'' and ''H'' are given as input, and one must determine whether ''G'' contains a subgraph that is isomorphic to ''H''. Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. However certain other cases of subgraph isomorphism may be solved in polynomial time. Sometimes the name subgraph matching is also used for the same problem. This name puts emphasis on finding such a subgraph as opposed to the bare decision problem. Decision problem and computational complexity To prove subgraph isomorphism is NP-complete, it must be formulated as a decision problem. The input to the decision problem is a pair of graphs ''G'' and ''H''. The answer to the problem is positive if ''H'' is isomorphic to a subgraph of ''G'', and negative otherwise. Formal question: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Product Of Graphs
In graph theory, the modular product of graphs ''G'' and ''H'' is a graph formed by combining ''G'' and ''H'' that has applications to subgraph isomorphism. It is one of several different kinds of graph products that have been studied, generally using the same vertex set (the Cartesian product of the sets of vertices of the two graphs ''G'' and ''H'') but with different rules for determining which edges to include. Definition The vertex set of the modular product of ''G'' and ''H'' is the cartesian product ''V''(''G'') × ''V''(''H''). Any two vertices (''u'', ''v'') and (''u' '', ''v' '') are adjacent in the modular product of ''G'' and ''H'' if and only if ''u'' is distinct from ''u' '', ''v'' is distinct from ''v' '', and either * ''u'' is adjacent with ''u' '' and ''v'' is adjacent with ''v' '', or * ''u'' is not adjacent with ''u' '' and ''v'' is not adjacent with ''v' ''. Application to subgraph isomorphism Cliques in the modular product graph correspo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Product Of Graphs
Cartesian means of or relating to the French philosopher René Descartes—from his Latinized name ''Cartesius''. It may refer to: Mathematics *Cartesian closed category, a closed category in category theory *Cartesian coordinate system, modern rectangular coordinate system * Cartesian diagram, a construction in category theory *Cartesian geometry, now more commonly called analytic geometry * Cartesian morphism, formalisation of ''pull-back'' operation in category theory *Cartesian oval, a curve *Cartesian product, a direct product of two sets *Cartesian product of graphs, a binary operation on graphs *Cartesian tree, a binary tree in computer science Philosophy *Cartesian anxiety, a hope that studying the world will give us unchangeable knowledge of ourselves and the world *Cartesian circle, a potential mistake in reasoning *Cartesian doubt, a form of methodical skepticism as a basis for philosophical rigor *Cartesian dualism, the philosophy of the distinction between mind and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domination Number
Domination or dominant may refer to: Society * World domination, which is mainly a conspiracy theory * Colonialism in which one group (usually a nation) invades another region for material gain or to eliminate competition * Chauvinism in which a person or group consider themselves to be superior, and thus entitled to use force to dominate others * Sexual dominance involving individuals in a subset of BDSM behaviour * Hierarchy * Patriarchy Music * Dominant (music), a diatonic scale step and diatonic function in tonal music theory * Dominant seventh chord, a four-note chord consisting of a major triad and a minor seventh * ''Domination'' (Cannonball Adderley album), 1965 * ''Domination'' (Domino album), 2004 * ''Domination'' (Morbid Angel album), 1995 * ''Domination'' (Morifade album), 2004 * "Domination", a song by Band-Maid from ''World Domination'' * " Domination", a song by Pantera from ''Cowboys from Hell'' * "Domination", a song by Symphony X from '' Paradise Lost ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vizing's Conjecture
In graph theory, Vizing's conjecture concerns a relation between the domination number and the cartesian product of graphs. This conjecture was first stated by , and states that, if denotes the minimum number of vertices in a dominating set for the graph , then : \gamma(G\,\Box\,H) \ge \gamma(G)\gamma(H). \, conjectured a similar bound for the domination number of the tensor product of graphs; however, a counterexample was found by . Since Vizing proposed his conjecture, many mathematicians have worked on it, with partial results described below. For a more detailed overview of these results, see . Examples A 4- cycle has domination number two: any single vertex only dominates itself and its two neighbors, but any pair of vertices dominates the whole graph. The product is a four-dimensional hypercube graph; it has 16 vertices, and any single vertex can only dominate itself and four neighbors, so three vertices could only dominate 15 of the 16 vertices. Therefore, at l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
