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Wiener–Araya Graph
The Wiener–Araya graph is, in graph theory, a graph on 42 vertices with 67 edges. It is hypohamiltonian, which means that it does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex from it is Hamiltonian. It is also planar. History Hypohamiltonian graphs were first studied by Sousselier in ''Problèmes plaisants et délectables'' (1963). In 1967, Lindgren built an infinite sequence of hypohamiltonian graphs. He first cited Gaudin, Herz and Rossi, then Busacker and Saaty as pioneers on this topic. From the start, the smallest hypohamiltonian graph is known: the Petersen graph. However, the hunt for the smallest planar hypohamiltonian graph continues. This question was first raised by 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 pu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypohamiltonian Graph
In the mathematical field of graph theory, a graph ''G'' is said to be hypohamiltonian if ''G'' itself does not have a Hamiltonian cycle but every graph formed by removing a single vertex from ''G'' is Hamiltonian. History Hypohamiltonian graphs were first studied by . cites and as additional early papers on the subject; another early work is by . sums up much of the research in this area with the following sentence: “The articles dealing with those graphs ... usually exhibit new classes of hypohamiltonian or hypotraceable graphs showing that for certain orders ''n'' such graphs indeed exist or that they possess strange and unexpected properties.” Applications Hypohamiltonian graphs arise in integer programming solutions to the traveling salesman problem: certain kinds of hypohamiltonian graphs define facets of the ''traveling salesman polytope'', a shape defined as the convex hull of the set of possible solutions to the traveling salesman problem, and these facets may ... [...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] |
Douglas Adams
Douglas Noel Adams (11 March 1952 – 11 May 2001) was an English author and screenwriter, best known for ''The Hitchhiker's Guide to the Galaxy''. Originally a 1978 BBC radio comedy, ''The Hitchhiker's Guide to the Galaxy'' developed into a "trilogy" of five books that sold more than 15 million copies in his lifetime. It was further developed into a television series, several stage plays, comics, a video game, and a 2005 feature film. Adams's contribution to UK radio is commemorated in The Radio Academy's Hall of Fame. Adams also wrote ''Dirk Gently's Holistic Detective Agency'' (1987) and ''The Long Dark Tea-Time of the Soul'' (1988), and co-wrote ''The Meaning of Liff'' (1983), ''The Deeper Meaning of Liff'' (1990), and ''Last Chance to See'' (1990). He wrote two stories for the television series ''Doctor Who'', co-wrote ''City of Death'' (1979), and served as script editor for its seventeenth season. He co-wrote the sketch "Patient Abuse" for the final episode of ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Hitchhiker's Guide To The Galaxy
''The Hitchhiker's Guide to the Galaxy'' (sometimes referred to as ''HG2G'', ''HHGTTG'', ''H2G2'', or ''tHGttG'') is a comic science fiction, comedy science fiction franchise created by Douglas Adams. Originally The Hitchhiker's Guide to the Galaxy (radio series), a 1978 radio comedy broadcast on BBC Radio 4, it was later adapted to other formats, including novels, stage shows, comic books, a The Hitchhiker's Guide to the Galaxy (TV series), 1981 TV series, a The Hitchhiker's Guide to the Galaxy (video game), 1984 text-based computer game, and The Hitchhiker's Guide to the Galaxy (film), 2005 feature film. ''The Hitchhiker's Guide to the Galaxy'' has become an international multi-media phenomenon; the novels are the most widely distributed, having been translated into more than 30 languages by 2005. The first novel, ''The Hitchhiker's Guide to the Galaxy (novel), The Hitchhiker's Guide to the Galaxy'' (1979), has been ranked fourth on the BBC’s The Big Read poll. The sixth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phrases From The Hitchhiker's Guide To The Galaxy
''The Hitchhiker's Guide to the Galaxy'' is a comic science fiction series created by Douglas Adams that has become popular among fans of the genre and members of the scientific community. Phrases from it are widely recognised and often used in reference to, but outside the context of, the source material. Many writers on popular science, such as Fred Alan Wolf, Paul Davies, and Michio Kaku, have used quotations in their books to illustrate facts about cosmology or philosophy. The Answer to the Ultimate Question of Life, the Universe, and Everything is 42 In the radio series and the first novel, a group of hyper-intelligent pan-dimensional beings demand to learn the Answer to the Ultimate Question of Life, The Universe, and Everything from the supercomputer Deep Thought, specially built for this purpose. It takes Deep Thought million years to compute and check the answer, which turns out to be 42. Deep Thought points out that the answer seems meaningless because the beings ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
42 (number)
42 (forty-two) is the natural number that follows 41 (number), 41 and precedes 43 (number), 43. Mathematics Forty-two (42) is a pronic number and an abundant number; its prime factorization (2\times 3\times 7) makes it the second sphenic number and also the second of the form (2\times 3\times r). Additional properties of the number 42 include: * It is the number of isomorphism classes of all simple and oriented directed graphs on 4 vertices. In other words, it is the number of all possible outcomes (up to isomorphism) of a tournament consisting of 4 teams where the game between any pair of teams results in three possible outcomes: the first team wins, the second team wins, or there is a draw. The group stage of the FIFA World cup is a good example. * It is the third primary pseudoperfect number. * It is a Catalan number. Consequently, 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered bina ... [...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] |
Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück, and Nigel Hitchin. Currently, the managing editor of Mathematische Annalen is Thomas Schick. Volumes 1–80 (1869–1919) were published by Teubner. Since 1920 (vol. 81), the journal has been published by Springer. In the late 1920s, under the editorship of Hilbert, the journal became embroiled in controversy over the participation of L. E. J. Brouwer on its editorial board, a spillover from the foundational Brouwer–Hilbert controversy. Between 1945 and 1947 the journal briefly ceased publication. References External links''Mathematische Annalen''homepage at Springer''Mathematische Annalen''archive (1869 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
105-Thomassen Graph
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planar Graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection. Plane graphs can be encoded by combinatorial maps or rotation systems. An equivalence class of topologically equivalent drawings on the sphere, usually with additional assumptions such as the absence of isthmuses, is called a pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
