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Neil Robertson (mathematician)
George Neil Robertson (born November 30, 1938) is a mathematician working mainly in topological graph theory, currently a distinguished professor emeritus at the Ohio State University. Education Robertson earned his B.Sc. from Brandon College in 1959 and his Ph.D. in 1969 at the University of Waterloo under his doctoral advisor William Tutte. Biography In 1969, Robertson joined the faculty of the Ohio State University, where he was promoted to Associate Professor in 1972 and Professor in 1984. He was a consultant with Bell Communications Research from 1984 to 1996. He has held visiting faculty positions in many institutions, most extensively at Princeton University from 1996 to 2001, and at Victoria University of Wellington, New Zealand, in 2002. He also holds an adjunct position at King Abdulaziz University in Saudi Arabia.. Research Robertson is known for his work in graph theory, and particularly for a long series of papers co-authored with Paul Seymour and published over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ohio State University
The Ohio State University (Ohio State or OSU) is a public university, public Land-grant university, land-grant research university in Columbus, Ohio, United States. A member of the University System of Ohio, it was founded in 1870. It is one of the List of largest United States university campuses by enrollment, largest universities by enrollment in the United States, with nearly 50,000 undergraduate students and nearly 15,000 graduate students. The university consists of sixteen colleges and offers over 400 degree programs at the undergraduate and Graduate school, graduate levels. It is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". the university has an List of colleges and universities in the United States by endowment, endowment of $7.9 billion. Its athletic teams compete in NCAA Division I as the Ohio State Buckeyes as a member of the Big Ten Conference for the majority of fielde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forbidden Minor
Forbidden may refer to: Science * Forbidden mechanism, a spectral line associated with absorption or emission of photons Films * ''Forbidden'' (1919 film), directed by Phillips Smalley and Lois Weber * ''Forbidden'' (1932 film), directed by Frank Capra * ''Forbidden'' (1949 film), directed by George King * ''Forbidden'' (1953 film), directed by Rudolph Maté * ''Forbidden'' (''Proibito''), a 1954 Italian film directed by Mario Monicelli * ''Forbidden'' (1984 film), directed by Anthony Page * '' The Forbidden'', a 2018 Uganda film Literature * ''Forbidden'' (Cooney novel), a 1994 novel by Caroline B. Cooney * ''Forbidden'' (Dekker and Lee novel), 2011 novel by Ted Dekker and Tosca Lee * ''Forbidden'', a 2010 novel by Tabitha Suzuma * "The Forbidden", short story by Clive Barker, from the Books of Blood Music * Forbidden (band), an American thrash metal band * ''Forbidden'' (Black Sabbath album) (1995), also the title track * ''Forbidden'' (Todrick Hall album) (2018), al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Graph
In graph theory, a perfect graph is a Graph (discrete mathematics), graph in which the Graph coloring, chromatic number equals the size of the maximum clique, both in the graph itself and in every induced subgraph. In all graphs, the chromatic number is greater than or equal to the size of the maximum clique, but they can be far apart. A graph is perfect when these numbers are equal, and remain equal after the deletion of arbitrary subsets of vertices. The perfect graphs include many important families of graphs and serve to unify results relating Graph coloring, colorings and cliques in those families. For instance, in all perfect graphs, the graph coloring problem, maximum clique problem, and maximum independent set problem can all be solved in polynomial time, despite their greater complexity for non-perfect graphs. In addition, several important minimax theorems in combinatorics, including Dilworth's theorem and Mirsky's theorem on partially ordered sets, Kőnig's theorem (gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strong Perfect Graph Theorem
In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither odd holes (odd-length induced cycles of length at least 5) nor odd antiholes (complements of odd holes). It was conjectured by Claude Berge in 1961. A proof by Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin Thomas was announced in 2002 and published by them in 2006. The proof of the strong perfect graph theorem won for its authors a $10,000 prize offered by Gérard Cornuéjols of Carnegie Mellon University and the 2009 Fulkerson Prize. Statement A perfect graph is a graph in which, for every induced subgraph, the size of the maximum clique equals the minimum number of colors in a coloring of the graph; perfect graphs include many well-known graph classes including the bipartite graphs, chordal graphs, and comparability graphs. In his 1961 and 1963 works defining for the first time this class of graphs, Claude ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maria Chudnovsky
Maria Chudnovsky (, ; born January 6, 1977) is an Israeli-American mathematician working on graph theory and combinatorial optimization. She is a 2012 MacArthur Fellow. Education and career Chudnovsky is a professor in the department of mathematics at Princeton University. She grew up in Russia (attended Saint Petersburg Lyceum 30) and Israel, studying at the Technion, and received her Ph.D. in 2003 from Princeton University under the supervision of Paul Seymour. After postdoctoral research at the Clay Mathematics Institute,. she became an assistant professor at Princeton University in 2005, and moved to Columbia University in 2006. By 2014, she was the Liu Family Professor of Industrial Engineering and Operations Research at Columbia. She returned to Princeton as a professor of mathematics in 2015. Chudnovsky is an editor for a number of mathematical journals, including ''Combinatorica'', '' Journal of Combinatorial Theory Series B'', ''Journal of Graph Theory'' and ''Proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four Color Theorem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions share a common boundary of non-zero length (i.e., not merely a corner where three or more regions meet). It was the first major theorem to be proved using a computer. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. The proof has gained wide acceptance since then, although some doubts remain. The theorem is a stronger version of the five color theorem, which can be shown using a significantly simpler argument. Although the weaker five color theorem was proven already in the 1800s, the four color theorem resisted until 1976 when it was proven by Kenneth Appel and Wolfgang Haken in a computer-aided proof. This came after many false proofs and mis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel P
Daniel commonly refers to: * Daniel (given name), a masculine given name and a surname * List of people named Daniel * List of people with surname Daniel * Daniel (biblical figure) * Book of Daniel, a biblical apocalypse, "an account of the activities and visions of Daniel" Daniel may also refer to: Arts and entertainment Literature * ''Daniel'' (Old English poem), an adaptation of the Book of Daniel * ''Daniel'', a 2006 novel by Richard Adams * ''Daniel'' (Mankell novel), 2007 Music * "Daniel" (Bat for Lashes song) (2009) * "Daniel" (Elton John song) (1973) * "Daniel", a song from '' Beautiful Creature'' by Juliana Hatfield * ''Daniel'' (album), a 2024 album by Real Estate Other arts and entertainment * ''Daniel'' (1983 film), by Sidney Lumet * ''Daniel'' (2019 film), a Danish film * Daniel (comics), a character in the ''Endless'' series Businesses * Daniel (department store), in the United Kingdom * H & R Daniel, a producer of English porcelain between 1827 and 18 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Coloring
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a Graph (discrete mathematics), graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color. Graph coloring is a special case of graph labeling. In its simplest form, it is a way of coloring the Vertex (graph theory), 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 (graph theory), edges 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 (graph theory), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hadwiger Conjecture (graph Theory)
In graph theory, the Hadwiger conjecture states that if G is loopless and has no K_t minor then its chromatic number satisfies It is known to be true for The conjecture is a generalization of the four color theorem and is considered to be one of the most important and challenging open problems in the field. In more detail, if all proper colorings of an undirected graph G use k or more colors, then one can find k disjoint connected subgraphs of G such that each subgraph is connected by an edge to each other subgraph. Contracting the edges within each of these subgraphs so that each subgraph collapses to a single vertex produces a complete graph K_k on k vertices as a minor The conjecture was made by Hugo Hadwiger in 1943. call it "one of the deepest unsolved problems in graph theory". Equivalent forms An equivalent form of the Hadwiger conjecture (the contrapositive of the form stated above) is that, if there is no sequence of edge contractions (each merging the two e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robin Thomas (mathematician)
Robin Thomas (August 22, 1962 – March 26, 2020) was a mathematician working in graph theory at the Georgia Institute of Technology. Thomas received his doctorate in 1985 from Charles University in Prague, Czechoslovakia (now the Czech Republic), under the supervision of Jaroslav Nešetřil. He joined the faculty at Georgia Tech in 1989, and became a Regents' Professor there, briefly serving as the department Chair. Personal life Thomas was married to Icelandic operations researcher Sigrún Andradóttir, also a professor at Georgia Tech. On March 26, 2020, he died of Amyotrophic Lateral Sclerosis at the age of 57 after 12 years of struggle with the illness. Awards Thomas was awarded the Fulkerson Prize for outstanding papers in discrete mathematics twice, in 1994 as co-author of a paper on the Hadwiger conjecture, and in 2009 for the proof of the strong perfect graph theorem. In 2011, he was awarded the Karel Janeček Foundation Neuron Prize for Lifetime Achievement in Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Girth (graph Theory)
In graph theory, the girth of an undirected graph is the length of a shortest Cycle (graph theory), cycle contained in the graph. If the graph does not contain any cycles (that is, it is a forest (graph theory), forest), its girth is defined to be infinity. For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3. A graph with girth four or more is triangle-free graph, triangle-free. Cages A cubic graph (all vertices have degree three) of girth that is as small as possible is known as a -cage (graph theory), cage (or as a -cage). The Petersen graph is the unique 5-cage (it is the smallest cubic graph of girth 5), the Heawood graph is the unique 6-cage, the McGee graph is the unique 7-cage and the Tutte eight cage is the unique 8-cage. There may exist multiple cages for a given girth. For instance there are three nonisomorphic 10-cages, each with 70 vertices: the Balaban 10-cage, the Harries graph and the Harries–Wong graph. Im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
