Reinhard Diestel (born 1959) [1] is a German mathematician specializing in graph theory, including the interplay among graph minors, matroid theory, tree decomposition, and infinite graphs. He holds the chair of discrete mathematics at the University of Hamburg. [2]
Diestel has a Ph.D. from the University of Cambridge in England, completed in 1986. [3] His dissertation, Simplicial Decompositions and Universal Graphs, was supervised by Béla Bollobás. [4]
He continued at Cambridge as a fellow of St. John's College, Cambridge until 1990. In 1994 he took a professorship at the Chemnitz University of Technology, and in 1999 he was given his current chair at the University of Hamburg. [3]
Diestel's books include:
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 combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats. In the language of partially ordered sets, a finite simple matroid is equivalent to a geometric lattice.
In graph theory, a branch of mathematics, the circuit rank, cyclomatic number, cycle rank, or nullity of an undirected graph is the minimum number of edges that must be removed from the graph to break all its cycles, making it into a tree or forest. It is equal to the number of independent cycles in the graph. Unlike the corresponding feedback arc set problem for directed graphs, the circuit rank r is easily computed using the formula
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants.
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges. The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often represented by 'roughly equal to' statements. Due to this, the way that density is defined often depends on the context of the problem.
In the mathematical field of graph theory, a path graph is a graph whose vertices can be listed in the order v1, v2, ..., vn such that the edges are {vi, vi+1} where i = 1, 2, ..., n − 1. Equivalently, a path with at least two vertices is connected and has two terminal vertices, while all others have degree 2.
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.
In graph theory, a connected graph G is said to be k-vertex-connected if it has more than k vertices and remains connected whenever fewer than k vertices are removed.
Martin Charles Golumbic is a mathematician and computer scientist known for his research on perfect graphs, graph sandwich problems, compiler optimization, and spatial-temporal reasoning. He is a professor emeritus of computer science at the University of Haifa, and was the founder of the journal Annals of Mathematics and Artificial Intelligence.
In graph theory, a Trémaux tree of an undirected graph is a type of spanning tree, generalizing depth-first search trees. They are defined by the property that every edge of connects an ancestor–descendant pair in the tree. Trémaux trees are named after Charles Pierre Trémaux, a 19th-century French author who used a form of depth-first search as a strategy for solving mazes. They have also been called normal spanning trees, especially in the context of infinite graphs.
In the mathematics of infinite graphs, an end of a graph represents, intuitively, a direction in which the graph extends to infinity. Ends may be formalized mathematically as equivalence classes of infinite paths, as havens describing strategies for pursuit–evasion games on the graph, or as topological ends of topological spaces associated with the graph.
Daniela Kühn is a German mathematician and the Mason Professor in Mathematics at the University of Birmingham in Birmingham, England. She is known for her research in combinatorics, and particularly in extremal combinatorics and graph theory.
Bruce Alan ReedFRSC is a Canadian mathematician and computer scientist, a former Canada Research Chair in Graph Theory at McGill University. His research is primarily in graph theory. He is a distinguished research fellow of the Institute of Mathematics in the Academia Sinica, Taiwan, and an adjunct professor at the University of Victoria in Canada.
In graph theory, a branch of mathematics, Halin's grid theorem states that the infinite graphs with thick ends are exactly the graphs containing subdivisions of the hexagonal tiling of the plane. It was published by Rudolf Halin, and is a precursor to the work of Robertson and Seymour linking treewidth to large grid minors, which became an important component of the algorithmic theory of bidimensionality.
Rudolf Halin was a German graph theorist, known for defining the ends of infinite graphs, for Halin's grid theorem, for extending Menger's theorem to infinite graphs, and for his early research on treewidth and tree decomposition. He is also the namesake of Halin graphs, a class of planar graphs constructed from trees by adding a cycle through the leaves of the given tree; earlier researchers had studied the subclass of cubic Halin graphs but Halin was the first to study this class of graphs in full generality.
Brigitte Irma Servatius is a mathematician specializing in matroids and structural rigidity. She is a professor of mathematics at Worcester Polytechnic Institute, and has been the editor-in-chief of the Pi Mu Epsilon Journal since 1999.
Ping Zhang is a mathematician specializing in graph theory. She is a professor of mathematics at Western Michigan University and the author of multiple textbooks on graph theory and mathematical proof.
Pearls in Graph Theory: A Comprehensive Introduction is an undergraduate-level textbook on graph theory by Nora Hartsfield and Gerhard Ringel. It was published in 1990 by Academic Press with a revised edition in 1994 and a paperback reprint of the revised edition by Dover Books in 2003. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
The Petersen Graph is a mathematics book about the Petersen graph and its applications in graph theory. It was written by Derek Holton and John Sheehan, and published in 1993 by the Cambridge University Press as volume 7 in their Australian Mathematical Society Lecture Series.
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