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David Sumner
David P. Sumner is an American mathematician known for his research in graph theory. He formulated Sumner's conjecture that tournaments are universal graphs for polytrees in 1971, and showed in 1974 that all claw-free graphs with an even number of vertices have perfect matchings. He and András Gyárfás independently formulated the Gyárfás–Sumner conjecture according to which, for every tree ''T'', the ''T''-free graphs are χ-bounded. Sumner earned his doctorate from the University of Massachusetts Amherst The University of Massachusetts Amherst (UMass Amherst, UMass) is a public research university in Amherst, Massachusetts and the sole public land-grant university in Commonwealth of Massachusetts. Founded in 1863 as an agricultural college, ... in 1970, under the supervision of David J. Foulis. He is a distinguished professor emeritus at the University of South Carolina.. References External linksHome page Year of birth missing (living people) Living peo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Massachusetts Amherst
The University of Massachusetts Amherst (UMass Amherst, UMass) is a public research university in Amherst, Massachusetts and the sole public land-grant university in Commonwealth of Massachusetts. Founded in 1863 as an agricultural college, it is the flagship and the largest campus in the University of Massachusetts system, as well as the first established. It is also a member of the Five College Consortium, along with four other colleges in the Pioneer Valley: Amherst College, Smith College, Mount Holyoke College, and Hampshire College. As of Fall 2022, UMass Amherst has an annual enrollment of more than 32,000 students, along with approximately 1,900 faculty members. It is the largest university in Massachusetts by campus size and second largest university by enrollment in Massachusetts, after Boston University. The university offers academic degrees in 109 undergraduate, 77 master's and 48 doctoral programs. Programs are coordinated in nine schools and colleges. The Universit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of South Carolina Faculty
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Massachusetts Amherst Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Year Of Birth Missing (living People)
A year or annus is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons are generally recognized: spring, summer, autumn and winter. In tropical and subtropical regions, several geographical sectors do not present defined seasons; but in the seasonal tropics, the annual wet and dry seasons are recognized and tracked. A calendar year is an approximation of the number of days of the Earth's orbital period, as counted in a given calendar. The Gregorian calendar, or modern calendar, presents its calendar year to be either a common year of 365 days or a leap year of 366 days, as do the Julian calendars. For the Gregorian calendar, the average length of the calendar year (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David J
David John Haskins (born 24 April 1957, Northampton, Northamptonshire, England), better known as David J, is a British alternative rock musician, producer, and writer. He is the bassist for the gothic rock band Bauhaus and for Love and Rockets. He has composed the scores for a number of plays and films, and also wrote and directed his own plays, ''Silver for Gold (The Odyssey of Edie Sedgwick)'', in 2008, which was restaged at REDCAT in Los Angeles in 2011, and ''The Chanteuse and The Devil's Muse'' in 2011. His artwork has been shown in galleries internationally, and he has been a resident DJ at venues such as the Knitting Factory. David J has released a number of singles and solo albums, and in 1990 he released one of the first No. 1 hits on the then nascent Modern Rock Tracks charts, with "I'll Be Your Chauffeur". His most recent single, "The Day That David Bowie Died" entered the UK vinyl singles chart at number 4 in 2016. The track appears on his double album, ''Vaga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
χ-bounded
In graph theory, a \chi-bounded family \mathcal of graphs is one for which there is some function c such that, for every integer t the graphs in \mathcal with t=\omega(G) (clique number) can be colored with at most c(t) colors. This concept and its notation were formulated by András Gyárfás. The use of the Greek letter chi in the term \chi-bounded is based on the fact that the chromatic number of a graph G is commonly denoted \chi(G). Nontriviality It is not true that the family of all graphs is \chi-bounded. As and showed, there exist triangle-free graphs of arbitrarily large chromatic number, so for these graphs it is not possible to define a finite value of t(3). Thus, \chi-boundedness is a nontrivial concept, true for some graph families and false for others. Specific classes Every class of graphs of bounded chromatic number is (trivially) \chi-bounded, with c(t) equal to the bound on the chromatic number. This includes, for instance, the planar graphs, the bipartite gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sumner's Conjecture
Sumner's conjecture (also called Sumner's universal tournament conjecture) states that every orientation of every n-vertex tree is a subgraph of every (2n-2)-vertex tournament. David Sumner, a graph theorist at the University of South Carolina, conjectured in 1971 that tournaments are universal graphs for polytrees. The conjecture was proven for all large n by Daniela Kühn, Richard Mycroft, and Deryk Osthus. Examples Let polytree P be a star K_, in which all edges are oriented outward from the central vertex to the leaves. Then, P cannot be embedded in the tournament formed from the vertices of a regular 2n-3-gon by directing every edge clockwise around the polygon. For, in this tournament, every vertex has indegree and outdegree equal to n-2, while the central vertex in P has larger outdegree n-1. Thus, if true, Sumner's conjecture would give the best possible size of a universal graph for polytrees. However, in every tournament of 2n-2 vertices, the average outdegree is n-\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree (graph Theory)
In graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ..., a tree is an undirected graph in which any two Vertex (graph theory), vertices are connected by ''exactly one'' Path (graph theory), path, or equivalently a Connected graph, connected Cycle (graph theory), acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by ''at most one'' path, or equivalently an acyclic undirected graph, or equivalently a Disjoint union of graphs, disjoint union of trees. A polytreeSee . (or directed tree or oriented treeSee .See . or singly connected networkSee .) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirecte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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