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 applications ranging from logic to statistical physics and from evolutionary biology to computer science.
Ronald Lewis Graham was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He was president of both the American Mathematical Society and the Mathematical Association of America, and his honors included the Leroy P. Steele Prize for lifetime achievement and election to the National Academy of Sciences.
In the mathematical field of graph theory, a Hamiltonian path is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding one more edge to form a Hamiltonian cycle, and removing any edge from a Hamiltonian cycle produces a Hamiltonian path. The computational problems of determining whether such paths and cycles exist in graphs are NP-complete; see Hamiltonian path problem for details.
Béla Bollobás FRS is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Paul Erdős since the age of 14.
Noga Alon is an Israeli mathematician and a professor of mathematics at Princeton University noted for his contributions to combinatorics and theoretical computer science, having authored hundreds of papers.
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 published extensively on topics in graph theory, combinatorics, and combinatorial optimization.
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.
The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies. Its study in Europe dates to the work of Leonardo Fibonacci in the 13th century AD, which introduced Arabian and Indian ideas to the continent. It has continued to be studied in the modern era.
Uppaluri Siva Ramachandra Murty, or U. S. R. Murty, is a Professor Emeritus of the Department of Combinatorics and Optimization, University of Waterloo.
Anton Kotzig was a Slovak–Canadian mathematician, expert in statistics, combinatorics and graph theory.
Carl Svante Janson is a Swedish mathematician. A member of the Royal Swedish Academy of Sciences since 1994, Janson has been the chaired professor of mathematics at Uppsala University since 1987.
Ivan Rival was a Canadian mathematician and computer scientist, a professor of mathematics at the University of Calgary and of computer science at the University of Ottawa.
Jon Hal Folkman was an American mathematician, a student of John Milnor, and a researcher at the RAND Corporation.
Michael S. Jacobson is a mathematician, and Professor of Mathematical & Statistical Sciences in the Department of Mathematical & Statistical Science at the University of Colorado Denver. He served as Chair from 2003 to 2012 and was on loan serving as a program director in EHR/DUE at the National Science Foundation.
Zdzisław Skupień is a Polish mathematician, expert in optimization, discrete mathematics, and graph theory, professor, dr. hab. (1982).
Nicholas Charles Wormald is an Australian mathematician and professor of mathematics at Monash University. He specializes in probabilistic combinatorics, graph theory, graph algorithms, Steiner trees, web graphs, mine optimization, and other areas in combinatorics.
In graph theory, a branch of mathematics, Fleischner's theorem gives a sufficient condition for a graph to contain a Hamiltonian cycle. It states that, if is a 2-vertex-connected graph, then the square of is Hamiltonian. It is named after Herbert Fleischner, who published its proof in 1974.
Michael David Plummer is a retired mathematics professor from Vanderbilt University. His field of work is in graph theory in which he has produced over a hundred papers and publications. He has also spoken at over a hundred and fifty guest lectures around the world.
Anthony J. W. Hilton is a British mathematician specializing in combinatorics and graph theory. His current positions are as emeritus professor of Combinatorial Mathematics at the University of Reading and professorial research fellow at Queen Mary College, University of London.
Leon Armenovich Takhtajan is a Russian mathematical physicist of Armenian descent, currently a professor of mathematics at the Stony Brook University, Stony Brook, NY, and a leading researcher at the Euler International Mathematical Institute, Saint Petersburg, Russia.
