Anthony J. W. Hilton (born 4 April 1941) is a British mathematician specializing in

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

and

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

. His current positions are as

emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". In some c ...

professor of Combinatorial Mathematics at the University of Reading and professorial research fellow at Queen Mary College, University of London.

Education

From 1951 to 1959, he attended the

Bedford School Bedford School is a 7–18 Single-sex education, boys Public school (United Kingdom), public school in the county town of Bedford in England. Founded in 1552, it is the oldest of four independent schools in Bedford run by the Harpur Trust. Bed ...

Bedford Bedford is a market town in Bedfordshire, England. At the 2011 Census, the population was 106,940. Bedford is the county town of Bedfordshire and seat of the Borough of Bedford local government district. Bedford was founded at a ford (crossin ...

Bedfordshire Bedfordshire (; abbreviated ''Beds'') is a Ceremonial County, ceremonial county in the East of England. It is bordered by Northamptonshire to the north, Cambridgeshire to the north-east, Hertfordshire to the south and the south-east, and Buckin ...

England England is a Countries of the United Kingdom, country that is part of the United Kingdom. It is located on the island of Great Britain, of which it covers about 62%, and List of islands of England, more than 100 smaller adjacent islands. It ...

. From there he attended

Reading University The University of Reading is a public research university in Reading, Berkshire, England. It was founded in 1892 as the University Extension College, Reading, an extension college of Christchurch College, Oxford, and became University College, ...

, where he earned a bachelor's degree in 1963 and was awarded a PhD in 1967.Hilton, Anthony
Personal Homepage
/ref> His dissertation was "Representation Theorems for Integers and Real Numbers" under his advisor David E. Daykin.Anthony Hilton
The Mathematics Genealogy Project

Work

Much of his work has been done in pioneering techniques in graph theory. He has discovered many results involving

Latin square Latin ( or ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken by the Latins in Latium (now known as Lazio), the lower Tiber area around Rome, Italy. Through the expansion o ...

s, including, which states that "if

n-1

cells of an

n\times n

matrix Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the m ...

are preassigned with no element repeated in any row or column then the remaining

n^2-n+1

cells can be filled so as to produce a Latin square." Another noteworthy result states that given a ''k''-

regular graph In graph theory, a regular graph is a Graph (discrete mathematics), graph where each Vertex (graph theory), vertex has the same number of neighbors; i.e. every vertex has the same Degree (graph theory), degree or valency. A regular directed graph ...

with

2n

vertices, if

k \geq 12n/7

then it is 1-factorizable. Chetwynd, A. G.; Hilton, A. J. W. (1985), "Regular graphs of high degree are 1-factorizable", Proceedings of the London Mathematical Society 50 (2): 193–206
doi:10.1112/plms/s3-50.2.193
In 1998, he was awarded the Euler Medal for "a distinguished career in the work he has produced, the people he has trained, and his leadership in the development of combinatorics in Britain." Among the specific things cited for are the creation of two new techniques for solving long standing problems. Through the use of edge colorings in the context of embedding graphs, he was able to settle the Evan's conjectureAnderson; Hilton (1980)
"Thank Evans!"
Proc. London Math. Soc., s3–47 (3) 507–522. and the Lindner conjecture. Through the use of graph amalgamations he was able to show many results, including a method for enumerating

Hamiltonian decomposition In graph theory, a branch of mathematics, a Hamiltonian decomposition of a given graph is a partition of the edges of the graph into Hamiltonian cycles. Hamiltonian decompositions have been studied both for undirected graphs and for directed grap ...

s as well as a

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 or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...

about embedding partial triple systems.Hilton; Roger (1990)
Edge-Colouring Graphs and Embedding Partial Triple Systems of Even Index
NATO ASI Series, Springer Netherlands, 301 pp 101-112

References

{{DEFAULTSORT:Hilton, Anthony 1941 births Living people 20th-century British mathematicians 21st-century British mathematicians Graph theorists