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Lovász Theta
Lovász (): * Lázár Lovász (born 1942), a Hungarian athlete who competed in hammer throw * László Lovász (born 1948, Budapest), a mathematician, best known for his work in combinatorics, **Lovász conjecture (1970) ** Erdős–Faber–Lovász conjecture (1972) ** The Lovász local lemma (proved in 1975, by László Lovász & P. Erdős) ** The Lenstra–Lenstra–Lovász lattice basis reduction (algorithm) (LLL) ** Algorithmic Lovász local lemma (proved in 2009, by Robin Moser and Gábor Tardos) ** Lovász number In graph theory, the Lovász number of a graph is a real number that is an upper bound on the Shannon capacity of the graph. It is also known as Lovász theta function and is commonly denoted by \vartheta(G), using a script form of the Greek letter ... (1979) {{DEFAULTSORT:Lovasz Hungarian-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lázár Lovász
Lázár Lovász (born May 24, 1942) is a retired Hungarian athlete who competed in hammer throw. He won a bronze medal at the 1968 Summer Olympics The 1968 Summer Olympics ( es, Juegos Olímpicos de Verano de 1968), officially known as the Games of the XIX Olympiad ( es, Juegos de la XIX Olimpiada) and commonly known as Mexico 1968 ( es, México 1968), were an international multi-sport eve ..., throwing 69.78 metres. References 1942 births Living people People from Suceava County Hungarian male hammer throwers Olympic athletes of Hungary Athletes (track and field) at the 1968 Summer Olympics Olympic bronze medalists for Hungary Medalists at the 1968 Summer Olympics Olympic bronze medalists in athletics (track and field) {{Hungary-athletics-bio-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
László Lovász
László Lovász (; born March 9, 1948) is a Hungarian mathematician and professor emeritus at Eötvös Loránd University, best known for his work in combinatorics, for which he was awarded the 2021 Abel Prize jointly with Avi Wigderson. He was the president of the International Mathematical Union from 2007 to 2010 and the president of the Hungarian Academy of Sciences from 2014 to 2020. In graph theory, Lovász's notable contributions include the proofs of Kneser's conjecture and the Lovász local lemma, as well as the formulation of the Erdős–Faber–Lovász conjecture. He is also one of the eponymous authors of the LLL lattice reduction algorithm. Early life and education Lovász was born on March 9, 1948, in Budapest, Hungary. Lovász attended the Fazekas Mihály Gimnázium in Budapest. He won three gold medals (1964–1966) and one silver medal (1963) at the International Mathematical Olympiad. He also participated in a Hungarian game show about math prodigies. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lovász Conjecture
In graph theory, the Lovász conjecture (1969) is a classical problem on Hamiltonian paths in graphs. It says: : Every finite connected vertex-transitive graph contains a Hamiltonian path. Originally László Lovász stated the problem in the opposite way, but this version became standard. In 1996, László Babai published a conjecture sharply contradicting this conjecture, but both conjectures remain widely open. It is not even known if a single counterexample would necessarily lead to a series of counterexamples. Historical remarks The problem of finding Hamiltonian paths in highly symmetric graphs is quite old. As Donald Knuth describes it in volume 4 of ''The Art of Computer Programming'', the problem originated in British campanology (bell-ringing). Such Hamiltonian paths and cycles are also closely connected to Gray codes. In each case the constructions are explicit. Variants of the Lovász conjecture Hamiltonian cycle Another version of Lovász conjecture states that : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Faber–Lovász Conjecture
In graph theory, the Erdős–Faber–Lovász conjecture is a problem about graph coloring, named after Paul Erdős, Vance Faber, and László Lovász, who formulated it in 1972.. It says: :If complete graphs, each having exactly vertices, have the property that every pair of complete graphs has at most one shared vertex, then the union of the graph (discrete mathematics), graphs can be properly colored with colors. A proof of the conjecture for all sufficiently large values of was announced in 2021 by Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus. Equivalent formulations introduced the problem with a story about seating assignment in committees: suppose that, in a university department, there are committees, each consisting of faculty members, and that all committees meet in the same room, which has chairs. Suppose also that at most one person belongs to the intersection of any two committees. Is it possible to assign the committee mem ... [...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] |
Lenstra–Lenstra–Lovász Lattice Basis Reduction Algorithm
The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982. Given a basis \mathbf = \ with ''n''-dimensional integer coordinates, for a lattice L (a discrete subgroup of R''n'') with d \leq n , the LLL algorithm calculates an ''LLL-reduced'' (short, nearly orthogonal) lattice basis in time \mathcal O(d^5n\log^3 B) where B is the largest length of \mathbf_i under the Euclidean norm, that is, B = \max\left(\, \mathbf_1\, _2, \, \mathbf_2\, _2, \dots, \, \mathbf_d\, _2\right). The original applications were to give polynomial-time algorithms for factorizing polynomials with rational coefficients, for finding simultaneous rational approximations to real numbers, and for solving the integer linear programming problem in fixed dimensions. LLL reduction The precise definition of LLL-reduced is as follows: Given a basis \mathbf=\, define its Gram–Sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmic Lovász Local Lemma
In theoretical computer science, the algorithmic Lovász local lemma gives an algorithmic way of constructing objects that obey a system of constraints with limited dependence. Given a finite set of ''bad'' events in a probability space with limited dependence amongst the ''Ai''s and with specific bounds on their respective probabilities, the Lovász local lemma proves that with non-zero probability all of these events can be avoided. However, the lemma is non-constructive in that it does not provide any insight on ''how'' to avoid the bad events. If the events are determined by a finite collection of mutually independent random variables, a simple Las Vegas algorithm with expected polynomial runtime proposed by Robin Moser and Gábor Tardos can compute an assignment to the random variables such that all events are avoided. Review of Lovász local lemma The Lovász Local Lemma is a powerful tool commonly used in the probabilistic method to prove the existence of certain co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lovász Number
In graph theory, the Lovász number of a graph is a real number that is an upper bound on the Shannon capacity of the graph. It is also known as Lovász theta function and is commonly denoted by \vartheta(G), using a script form of the Greek letter theta to contrast with the upright theta used for Shannon capacity. This quantity was first introduced by László Lovász in his 1979 paper ''On the Shannon Capacity of a Graph''. Accurate numerical approximations to this number can be computed in polynomial time by semidefinite programming and the ellipsoid method. It is sandwiched between the chromatic number and clique number of any graph, and can be used to compute these numbers on graphs for which they are equal, including perfect graphs. Definition Let G=(V,E) be a graph on n vertices. An ordered set of n unit vectors U=(u_i\mid i\in V)\subset\mathbb^N is called an orthonormal representation of G in \mathbb^N, if u_i and u_j are orthogonal whenever vertices i and j are not adjac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
