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Tibor Gallai
Tibor Gallai (born Tibor Grünwald, 15 July 1912 – 2 January 1992) was a Hungarian mathematician. He worked in combinatorics, especially in graph theory, and was a lifelong friend and collaborator of Paul Erdős. He was a student of Dénes Kőnig and an advisor of László Lovász. He was a corresponding member of the Hungarian Academy of Sciences (1991). His main results The Edmonds–Gallai decomposition theorem, which was proved independently by Gallai and Jack Edmonds, describes finite graphs from the point of view of matchings. Gallai also proved, with Milgram, Dilworth's theorem in 1947, but as they hesitated to publish the result, Dilworth independently discovered and published it.P. ErdősIn memory of Tibor Gallai ''Combinatorica'', 12(1992), 373–374. Gallai was the first to prove the higher-dimensional version of van der Waerden's theorem. With Paul Erdős he gave a necessary and sufficient condition for a sequence to be the degree sequence of a graph, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budapest
Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population of 1,752,286 over a land area of about . Budapest, which is both a city and county, forms the centre of the Budapest metropolitan area, which has an area of and a population of 3,303,786; it is a primate city, constituting 33% of the population of Hungary. The history of Budapest began when an early Celtic settlement transformed into the Roman town of Aquincum, the capital of Lower Pannonia. The Hungarians arrived in the territory in the late 9th century, but the area was pillaged by the Mongols in 1241–42. Re-established Buda became one of the centres of Renaissance humanist culture by the 15th century. The Battle of Mohács, in 1526, was followed by nearly 150 years of Ottoman rule. After the reconquest of Buda in 1686, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jack Edmonds
Jack R. Edmonds (born April 5, 1934) is an American-born and educated computer scientist and mathematician who lived and worked in Canada for much of his life. He has made fundamental contributions to the fields of combinatorial optimization, polyhedral combinatorics, discrete mathematics and the theory of computing. He was the recipient of the 1985 John von Neumann Theory Prize. Early career Edmonds attended Duke University before completing his undergraduate degree at George Washington University in 1957. He thereafter received a master's degree in 1960 at the University of Maryland under Bruce L. Reinhart with a thesis on the problem of embedding graphs into surfaces. From 1959 to 1969 he worked at the National Institute of Standards and Technology (then the National Bureau of Standards), and was a founding member of Alan J. Goldman, Alan Goldman’s newly created Operations Research Section in 1961. Goldman proved to be a crucial influence by enabling Edmonds to work in a RAND ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Members Of The Hungarian Academy Of Sciences
Member may refer to: * Military jury, referred to as "Members" in military jargon * Element (mathematics), an object that belongs to a mathematical set * In object-oriented programming, a member of a class ** Field (computer science), entries in a database ** Member variable, a variable that is associated with a specific object * Limb (anatomy), an appendage of the human or animal body ** Euphemism for penis * Structural component of a truss, connected by nodes * User (computing), a person making use of a computing service, especially on the Internet * Member (geology), a component of a geological formation * Member of parliament * The Members, a British punk rock band * Meronymy, a semantic relationship in linguistics * Church membership, belonging to a local Christian congregation, a Christian denomination and the universal Church * Member, a participant in a club or learned society A learned society (; also learned academy, scholarly society, or academic association) is an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1992 Deaths
Year 199 ( CXCIX) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was sometimes known as year 952 ''Ab urbe condita''. The denomination 199 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Mesopotamia is partitioned into two Roman provinces divided by the Euphrates, Mesopotamia and Osroene. * Emperor Septimius Severus lays siege to the city-state Hatra in Central-Mesopotamia, but fails to capture the city despite breaching the walls. * Two new legions, I Parthica and III Parthica, are formed as a permanent garrison. China * Battle of Yijing: Chinese warlord Yuan Shao defeats Gongsun Zan. Korea * Geodeung succeeds Suro of Geumgwan Gaya, as king of the Korean kingdom of Gaya (traditional date). By topic Religion * Pope Zephyrinus succeeds Pope Victor I, as th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1912 Births
Year 191 ( CXCI) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Apronianus and Bradua (or, less frequently, year 944 ''Ab urbe condita''). The denomination 191 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Parthia * King Vologases IV of Parthia dies after a 44-year reign, and is succeeded by his son Vologases V. China * A coalition of Chinese warlords from the east of Hangu Pass launches a punitive campaign against the warlord Dong Zhuo, who seized control of the central government in 189, and held the figurehead Emperor Xian hostage. After suffering some defeats against the coalition forces, Dong Zhuo forcefully relocates the imperial capital from Luoyang to Chang'an. Before leaving, Dong Zhuo orders his troops to loot the tombs of the H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gallai–Edmonds Decomposition
In graph theory, the Gallai–Edmonds decomposition is a partition of the vertices of a graph into three subsets which provides information on the structure of maximum matchings in the graph. Tibor Gallai and Jack Edmonds independently discovered it and proved its key properties. The Gallai–Edmonds decomposition of a graph can be found using the blossom algorithm. Properties Given a graph G, its Gallai–Edmonds decomposition consists of three disjoint sets of vertices, A(G), C(G), and D(G), whose union is V(G): the set of all vertices of G. First, the vertices of G are divided into ''essential vertices'' (vertices which are covered by every maximum matching in G) and ''inessential vertices'' (vertices which are left uncovered by at least one maximum matching in G). The set D(G) is defined to contain all the inessential vertices. Essential vertices are split into A(G) and C(G): the set A(G) is defined to contain all essential vertices adjacent to at least one vertex of D(G) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gallai–Hasse–Roy–Vitaver Theorem
In graph theory, the Gallai–Hasse–Roy–Vitaver theorem is a form of duality between the colorings of the vertices of a given undirected graph and the orientations of its edges. It states that the minimum number of colors needed to properly color any graph G equals one plus the length of a longest path in an orientation of G chosen to minimize this path's The orientations for which the longest path has minimum length always include at least one This theorem implies that every orientation of a graph with contains a simple directed path with this path can be constrained to begin at any vertex that can reach all other vertices of the oriented Examples A bipartite graph may be oriented from one side of the bipartition to the other. The longest path in this orientation has length two, with only two vertices. Conversely, if a graph is oriented without any three-vertex paths, then every vertex must either be a source (with no incoming edges) or a sink (with no outgoing edges) an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Gallai Theorem
The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics. It provides one of two known approaches to solving the graph realization problem, i.e. it gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph. A sequence obeying these conditions is called "graphic". The theorem was published in 1960 by Paul Erdős and Tibor Gallai, after whom it is named. Statement A sequence of non-negative integers d_1\geq\cdots\geq d_n can be represented as the degree sequence of a finite simple graph on ''n'' vertices if and only if d_1+\cdots+d_n is even and : \sum^_d_i\leq k(k-1)+ \sum^n_ \min (d_i,k) holds for every k in 1\leq k\leq n. Proofs It is not difficult to show that the conditions of the Erdős–Gallai theorem are necessary for a sequence of numbers to be graphic. The requirement that the sum of the degrees be even is the handshaking lemma, already used by Euler in his 17 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necessary And Sufficient Condition
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of is guaranteed by the truth of (equivalently, it is impossible to have without ). Similarly, is sufficient for , because being true always implies that is true, but not being true does not always imply that is not true. In general, a necessary condition is one that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition. The assertion that a statement is a "necessary ''and'' sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false. In ordinary English (also natural language) "necessary" and "sufficient" indicate relations betw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Waerden's Theorem
Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory. Van der Waerden's theorem states that for any given positive integers ''r'' and ''k'', there is some number ''N'' such that if the integers are colored, each with one of ''r'' different colors, then there are at least ''k'' integers in arithmetic progression whose elements are of the same color. The least such ''N'' is the Van der Waerden number ''W''(''r'', ''k''), named after the Dutch mathematician B. L. van der Waerden. Example For example, when ''r'' = 2, you have two colors, say and . ''W''(2, 3) is bigger than 8, because you can color the integers from like this: and no three integers of the same color form an arithmetic progression. But you can't add a ninth integer to the end without creating such a progression. If you add a , then the , , and are in arithmetic progression. Alternatively, if you add a , then the , , and are in arithmetic progression. In fact, there is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorica
''Combinatorica'' is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science. It started in 1981, with László Babai and László Lovász as the editors-in-chief with Paul Erdős as honorary editor-in-chief. The current editors-in-chief are Imre Bárány and József Solymosi. The advisory board consists of Ronald Graham, Gyula O. H. Katona, Miklós Simonovits, Vera Sós, and Endre Szemerédi. It is published by the János Bolyai Mathematical Society and Springer Verlag. The following members of the '' Hungarian School of Combinatorics'' have strongly contributed to the journal as authors, or have served as editors: Miklós Ajtai, László Babai, József Beck, András Frank, Péter Frankl, Zoltán Füredi, András Hajnal, Gyula Katona, László Lovász, László Pyber, Alexander Schrijver, Miklós Simonovits, Vera Sós, Endre Szemerédi, Tamás Szőnyi, Éva Tardos, Gábor Tardos.{{cite web, url=https://www.springer.com/ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
