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András Hajnal
András Hajnal (May 13, 1931 – July 30, 2016) was a professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics. Biography Hajnal was born on 13 May 1931,Curriculum vitae in , . He received his university diploma (M.Sc. degree) in 1953 from the , his |
Rutgers University
Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and was affiliated with the Reformed Church in America, Dutch Reformed Church. It is the eighth-oldest college in the United States, the second-oldest in New Jersey (after Princeton University), and one of the nine U.S. colonial colleges that were chartered before the American Revolution.Stoeckel, Althea"Presidents, professors, and politics: the colonial colleges and the American revolution", ''Conspectus of History'' (1976) 1(3):45–56. In 1825, Queen's College was renamed Rutgers College in honor of Colonel Henry Rutgers, whose substantial gift to the school had stabilized its finances during a period of uncertainty. For most of its existence, Rutgers was a Private university, private liberal arts college but it has evolved int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Erdős
Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics. Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clique (graph Theory)
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] |
Discrete Mathematics (journal)
''Discrete Mathematics'' is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West ( University of Illinois, Urbana). History The journal was established in 1971. The very first article it published was written by Paul Erdős, who went on to publish a total of 84 papers in the journal. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 0.87. Notable publications * The 1972 ... [...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] |
Journal Of Graph Theory
The ''Journal of Graph Theory'' is a peer-reviewed mathematics journal specializing in graph theory and related areas, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. It is published by John Wiley & Sons. The journal was established in 1977 by Frank Harary.Frank Harary a biographical sketch at the ACM site The are [...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] |
Equitable Coloring
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that *No two adjacent vertices have the same color, and *The numbers of vertices in any two color classes differ by at most one. That is, the partition of vertices among the different colors is as uniform as possible. For instance, giving each vertex a distinct color would be equitable, but would typically use many more colors than are necessary in an optimal equitable coloring. An equivalent way of defining an equitable coloring is that it is an embedding of the given graph as a subgraph of a Turán graph with the same set of vertices. There are two kinds of chromatic number associated with equitable coloring.. The equitable chromatic number of a graph ''G'' is the smallest number ''k'' such that ''G'' has an equitable coloring with ''k'' colors. But ''G'' might not have equitable colorings for some larger numbers of colors; the equitable c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hajnal–Szemerédi Theorem
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that *No two adjacent vertices have the same color, and *The numbers of vertices in any two color classes differ by at most one. That is, the partition of vertices among the different colors is as uniform as possible. For instance, giving each vertex a distinct color would be equitable, but would typically use many more colors than are necessary in an optimal equitable coloring. An equivalent way of defining an equitable coloring is that it is an embedding of the given graph as a subgraph of a Turán graph with the same set of vertices. There are two kinds of chromatic number associated with equitable coloring.. The equitable chromatic number of a graph ''G'' is the smallest number ''k'' such that ''G'' has an equitable coloring with ''k'' colors. But ''G'' might not have equitable colorings for some larger numbers of colors; the equitable c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (mathematics)
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majority Function
In Boolean logic, the majority function (also called the median operator) is the Boolean function that evaluates to false when half or more arguments are false and true otherwise, i.e. the value of the function equals the value of the majority of the inputs. Representing true values as 1 and false values as 0, we may use the (real-valued) formula: :\langle p_1,\dots,p_n \rangle = \operatorname \left ( p_1,\dots,p_n \right ) = \left \lfloor \frac + \frac \right \rfloor. The "−1/2" in the formula serves to break ties in favor of zeros when the number of arguments ''n'' is even. If the term "−1/2" is omitted, the formula can be used for a function that breaks ties in favor of ones. Most applications deliberately force an odd number of inputs so they don't have to deal with the question of what happens when exactly half the inputs are 0 and exactly half the inputs are 1. The few systems that calculate the majority function on an even number of inputs are often biased to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
