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Heawood Graph And Map On Torus
Heawood is a surname. Notable people with the surname include: *Jonathan Heawood, British journalist *Percy John Heawood (1861–1955), British mathematician **Heawood conjecture **Heawood graph **Heawood number See also *Heywood (surname) {{surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jonathan Heawood
Jonathan Heawood is an English journalist and literary editor. He is Executive Director of thPublic Interest News Foundation the first journalism charity in the UK to be awarded charitable status. Heawood is the founder and former CEO of IMPRESS, the only press regulator recognised under Royal Charter in the United Kingdom. He is a former Director of Programmes at the Sigrid Rausing Trust, a private human rights foundation, Director of the English Centre of International PEN, deputy literary editor of ''The Observer'' and editor of the '' Fabian Review''. He writes on cultural and political issues for a number of publications, including the ''Telegraph'', ''Independent'', ''The Guardian'', ''London Review of Books'' and ''New Statesman''. He is married to writer Amy Jenkins and they have one child. He is the great grandson of Percy John Heawood Percy John Heawood (8 September 1861 – 24 January 1955) was a British mathematician, who concentrated on graph colouring. Li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percy John Heawood
Percy John Heawood (8 September 1861 – 24 January 1955) was a British mathematician, who concentrated on graph colouring. Life He was the son of the Rev. John Richard Heawood of Newport, Shropshire, and his wife Emily Heath, daughter of the Rev. Joseph Heath of Wigmore, Herefordshire; and a first cousin of Oliver Lodge, whose mother Grace was also a daughter of Joseph Heath. He was educated at Queen Elizabeth's School, Ipswich, and matriculated at Exeter College, Oxford in 1880, graduating B.A. in 1883 and M.A. in 1887. Heawood spent his academic career at Durham University, where he was appointed Lecturer in 1885. He was, successively, Censor of St Cuthbert's Society between 1897 and 1901 succeeding Frank Byron Jevons in the role, Senior Proctor of the university from 1901, Professor in 1910 and Vice-Chancellor between 1926 and 1928. He was awarded an OBE, as Honorary Secretary of the Preservation Fund, for his part in raising £120,000 to prevent Durham Castle from col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heawood Conjecture
In graph theory, the Heawood conjecture or Ringel–Youngs theorem gives a lower bound for the number of colors that are necessary for graph coloring on a surface of a given genus. For surfaces of genus 0, 1, 2, 3, 4, 5, 6, 7, ..., the required number of colors is 4, 7, 8, 9, 10, 11, 12, 12, .... , the chromatic number or Heawood number. The conjecture was formulated in 1890 by Percy John Heawood and proven in 1968 by Gerhard Ringel and Ted Youngs. One case, the non-orientable Klein bottle, proved an exception to the general formula. An entirely different approach was needed for the much older problem of finding the number of colors needed for the plane or sphere, solved in 1976 as the four color theorem by Haken and Appel. On the sphere the lower bound is easy, whereas for higher genera the upper bound is easy and was proved in Heawood's original short paper that contained the conjecture. In other words, Ringel, Youngs and others had to construct extreme examples for every ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heawood Graph
Heawood is a surname. Notable people with the surname include: *Jonathan Heawood, British journalist *Percy John Heawood (1861–1955), British mathematician **Heawood conjecture **Heawood graph **Heawood number In mathematics, the Heawood number of a surface is an upper bound for the number of colors that suffice to color any graph embedded in the surface. In 1890 Heawood proved for all surfaces ''except'' the sphere that no more than : H(S)=\left\lfl ... See also * Heywood (surname) {{surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heawood Number
In mathematics, the Heawood number of a surface is an upper bound for the number of colors that suffice to color any graph embedded in the surface. In 1890 Heawood proved for all surfaces ''except'' the sphere that no more than : H(S)=\left\lfloor\frac\right\rfloor = \left\lfloor\frac\right\rfloor colors are needed to color any graph embedded in a surface of Euler characteristic e(S), or genus g(S) for an orientable surface. The number H(S) became known as Heawood number in 1976. Franklin proved that the chromatic number of a graph embedded in the Klein bottle can be as large as 6, but never exceeds 6. Later it was proved in the works of Gerhard Ringel, J. W. T. Youngs, and other contributors that the complete graph with H(S) vertices can be embedded in the surface S unless S is the Klein bottle. This established that Heawood's bound could not be improved. For example, the complete graph on 7 vertices can be embedded in the torus as follows: The case of the sphere is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
