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Fleischner's Theorem
In graph theory, a branch of mathematics, Fleischner's theorem gives a sufficient condition for a graph to contain a Hamiltonian cycle. It states that, if is a 2-vertex-connected graph, then the square of is Hamiltonian. it is named after Herbert Fleischner, who published its proof in 1974. Definitions and statement An undirected graph ''G'' is Hamiltonian if it contains a cycle that touches each of its vertices exactly once. It is 2-vertex-connected if it does not have an articulation vertex, a vertex whose deletion would leave the remaining graph disconnected. Not every 2-vertex-connected graph is Hamiltonian; counterexamples include the Petersen graph and the complete bipartite graph ''K''2,3. The square of ''G'' is a graph ''G''2 that has the same vertex set as ''G'', and in which two vertices are adjacent if and only if they have distance at most two in ''G''. Fleischner's theorem states that the square of a finite 2-vertex-connected graph with at least three vertices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fleischner's Theorem
In graph theory, a branch of mathematics, Fleischner's theorem gives a sufficient condition for a graph to contain a Hamiltonian cycle. It states that, if is a 2-vertex-connected graph, then the square of is Hamiltonian. it is named after Herbert Fleischner, who published its proof in 1974. Definitions and statement An undirected graph ''G'' is Hamiltonian if it contains a cycle that touches each of its vertices exactly once. It is 2-vertex-connected if it does not have an articulation vertex, a vertex whose deletion would leave the remaining graph disconnected. Not every 2-vertex-connected graph is Hamiltonian; counterexamples include the Petersen graph and the complete bipartite graph ''K''2,3. The square of ''G'' is a graph ''G''2 that has the same vertex set as ''G'', and in which two vertices are adjacent if and only if they have distance at most two in ''G''. Fleischner's theorem states that the square of a finite 2-vertex-connected graph with at least three vertices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "punctures" or "missing endpoints", i.e. that the space not exclude any ''limiting values'' of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval ,1would be compact. Similarly, the space of rational numbers \mathbb is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers \mathbb is not compact either, because it excludes the two limiting values +\infty and -\infty. However, the ''extended'' real number line ''would'' be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other topologic ... [...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] |
Journal Of Combinatorial Theory
The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applications of combinatorics. ''Series B'' is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and are widely known as ''JCTA'' and ''JCTB''. The journal was founded in 1966 by Frank Harary and Gian-Carlo Rota.They are acknowledged on the journals' title pages and Web sites. SeEditorial board of JCTA Originally there was only one journal, which was split into two parts in 1971 as the field grew rapidly. An electronic, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Important examples Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, ''b'', and ''c'' can satisfy the equation ''a^n + b^n = c^n'' for any integer value of ''n'' greater than two. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of '' Arithmetica'', where he claimed that he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Toughness
Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discrete mathematics *Graph of a function *Graph of a relation *Graph paper *Chart, a means of representing data (also called a graph) Computing * Graph (abstract data type), an abstract data type representing relations or connections *graph (Unix), Unix command-line utility *Conceptual graph, a model for knowledge representation and reasoning Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also *Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy (suffix from the Greek for "describe," "write" or "draw") *List of information graphics software *Statistical graphics Statistical graphics, also known as statistical graphical techniques, are graphi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Václav Chvátal
Václav (Vašek) Chvátal () is a Professor Emeritus in the Department of Computer Science and Software Engineering at Concordia University in Montreal, Quebec, Canada and a Visiting Professor at Charles University in Prague. He has published extensively on topics in graph theory, combinatorics, and combinatorial optimization. Biography Chvátal was born in 1946 in Prague and educated in mathematics at Charles University in Prague, where he studied under the supervision of Zdeněk Hedrlín. He fled Czechoslovakia in 1968, three days after the Soviet invasion, and completed his Ph.D. in Mathematics at the University of Waterloo, under the supervision of Crispin St. J. A. Nash-Williams, in the fall of 1970. Subsequently, he took positions at McGill University (1971 and 1978-1986), Stanford University (1972 and 1974-1977), the Université de Montréal (1972-1974 and 1977-1978), and Rutgers University (1986-2004) before returning to Montreal for the Canada Research Chair in Combi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael D
Michael D may refer to: * Mike D (born 1965), founding member of the Beastie Boys Arts * Michael D. Cohen (actor) (born 1975), Canadian actor * Michael D. Ellison, African American recording artist * Michael D. Fay, American war artist * Michael D. Ford (1928–2018), English set decorator * Michael D. Roberts, American actor Business * Michael D. Dingman (1931–2017), American businessman * Michael D. Ercolino (1906–1982), American businessman * Michael D. Fascitelli, (born c. 1957), American businessman * Michael D. Penner (born 1969), Canadian lawyer and businessman Education * Michael D. Aeschliman (born 1948), American–Swiss educator * Michael D. Cohen (academic) (1945–2013), professor of complex systems, information and public policy at the University of Michigan * Michael D. Hanes, American music educator * Michael D. Hurley (born 1976), British Professor of Literature and Theology * Michael D. Johnson, a former President of John Carroll University * Mic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crispin Nash-Williams
Crispin St John Alvah Nash-Williams FRSE (19 December 1932 – 20 January 2001) was a British mathematician. His research interest was in the field of discrete mathematics, especially graph theory. Biography Nash-Williams was born on 19 December 1932 in Cardiff, Wales. His father, Victor Erle Nash-Williams ( Williams), was an archaeologist at University College Cardiff, and his mother had studied classics at Oxford. As a small boy, Nash-Williams attended Christ Church Cathedral School in Oxford, which was then headed by Wilfrid Oldaker. A biographer has said that Oldaker was a formative influence on Nash-Williams.D. J. A. Welsh"Crispin St J. A. Nash-Williams (1932–2001)"in ''Bulletin of the London Mathematical Society'', Vol. 35, Issue 6, November 2003, Pages 829–844 After studying mathematics at the University of Cambridge, earning the title of Senior Wrangler in 1953, he remained at Cambridge for his graduate studies, under the supervision of Shaun Wylie and David Rees. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric Space
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different branches of mathematics. Many types of mathematical objects have a natural notion of distance and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bottleneck Traveling Salesman Problem
The Bottleneck traveling salesman problem (bottleneck TSP) is a problem in discrete or combinatorial optimization. The problem is to find the Hamiltonian cycle (visiting each node exactly once) in a weighted graph which minimizes the weight of the highest-weight edge of the cycle.. It was first formulated by with some additional constraints, and in its full generality by . Complexity The problem is known to be NP-hard. The decision problem version of this, "for a given length is there a Hamiltonian cycle in a graph with no edge longer than ?", is NP-complete. NP-completeness follows immediately by a reduction from the problem of finding a Hamiltonian cycle.. Algorithms Another reduction, from the bottleneck TSP to the usual TSP (where the goal is to minimize the sum of edge lengths), allows any algorithm for the usual TSP to also be used to solve the bottleneck TSP. If the edge weights of the bottleneck TSP are replaced by any other numbers that have the same relative order, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
