631 articles
Gosset polytope
A Gosset polytope is one of a family of semiregular polytopes in six, seven, and eight dimensions discovered by Thorold Gosset in 1900, the most famous being the eight-dimensional 421 polytope.
Gowers norm
The Gowers norm, or Gowers uniformity norm, is a measure of how far a function on a finite group deviates from a low-degree polynomial phase, introduced by Timothy Gowers in 1998.
Graceful labeling
A graceful labeling assigns graph vertices distinct integers from 0 to q so that the edge differences are also distinct; whether every tree has one is open.
Graeco-Latin square
A Graeco-Latin square, also called an Euler square, is an n × n array formed by superimposing two orthogonal Latin squares, named by Euler in 1782.
Graph (discrete mathematics)
A graph in discrete mathematics is a structure of vertices joined by edges that models relationships; its study, graph theory, dates to Euler's 1736 Königsberg analysis.
Graph drawing
Graph drawing, also called graph layout, is the branch of computer science that positions graph vertices and routes edges to render networks as readable diagrams.
Graph embedding
A graph embedding is a placement of a graph on a surface with vertices as points and edges as noncrossing curves, the central object of topological graph theory.
Graph Fourier transform
The graph Fourier transform decomposes a signal defined on a graph's vertices into components carried by the eigenvectors of the graph Laplacian, like the classical Fourier transform.
Graph invariant
A graph invariant, also called a graph property, is a quantity of a graph that depends only on its structure, not on vertex labels or how it is drawn.
Graph isomorphism
Graph isomorphism, also called testing isomorphic graphs, asks whether two graphs have the same structure up to renaming vertices; László Babai's 2015 quasipolynomial algorithm was a major breakthrough.
Graph isomorphism problem
The graph isomorphism problem asks whether two graphs can be relabeled to be identical. It lies in NP, and László Babai gave a quasipolynomial-time algorithm in 2015.
Graph minor
A graph minor is a graph derived from another by deleting or contracting edges and removing isolated vertices; Robertson and Seymour developed the theory of it.
Graph partitioning
Graph partitioning divides a graph's vertices into roughly equal blocks while minimizing the edges crossing between blocks, an NP-hard problem used in parallel computing and VLSI design.
Graph removal lemma
The graph removal lemma is a theorem in extremal graph theory: a graph with few copies of a fixed graph H can be made H-free by deleting few edges.
Graph spectrum
The graph spectrum is the set of eigenvalues of a graph's adjacency matrix, real because the matrix is symmetric, and the subject of spectral graph theory.
Graph structure theorem
The graph structure theorem, proved by Neil Robertson and Paul Seymour, describes every graph with no fixed graph H as a minor as built from pieces embeddable in a surface.
Graph theory
Graph theory is the branch of mathematics that studies graphs, structures of vertices and edges modeling pairwise relationships, originating in Euler's 1735 analysis of the Königsberg bridges problem.
Graph Theory with Applications
Graph Theory with Applications is a graduate-level graph theory textbook by J. A. Bondy and U. S. R. Murty, published in 1976 and praised by reviewers as outstanding.
Graphic matroid
The graphic matroid, also called the cycle matroid, is the matroid on a graph's edges whose independent sets are forests and whose bases are spanning trees.
Graphon
A graphon is a symmetric measurable function on the unit square serving as the limit object for convergent sequences of dense graphs, introduced by Lovász and Szegedy in 2004.
Graphviz
Graphviz is open source graph visualization software that turns textual descriptions of abstract graphs into automatically arranged diagrams; it originated at AT&T Bell Laboratories and is used in software engineering, bioinformatics, and machine learning.
Greedy coloring
Greedy coloring, also called the first-fit algorithm, is a simple graph coloring method that processes vertices in a chosen order, giving each the smallest color its already-colored neighbors lack.
Green–Tao theorem
The Green–Tao theorem is a result in number theory proved by Ben Green and Terence Tao in 2004, stating that the prime numbers contain arbitrarily long arithmetic progressions.
Group divisible design
A group divisible design (GDD) is a combinatorial design whose point set is split into groups, with cross-group pairs of points appearing together in a constant number of blocks.
Gurobi Optimization
Gurobi Optimization is an optimization software company co-founded in 2008 by Robert Bixby, Zonghao Gu, and Edward Rothberg, named from the first two letters of their surnames.
H-vector
An h-vector is a sequence of integers encoding the number of faces of a simplicial complex, polytope, or poset in each dimension; it determines, and is determined by, the f-vector.
Hadwiger conjecture (graph theory)
Hadwiger's conjecture, proposed by Hugo Hadwiger in 1943, states that every graph with no complete graph Kt as a minor can be colored with t − 1 colors.
Hadwiger–Nelson problem
The Hadwiger–Nelson problem, or chromatic number of the plane, asks the fewest colors needed so points a unit distance apart differ, known to be 5, 6, or 7.
Hall's marriage theorem
Hall's marriage theorem, proved by Philip Hall in 1935, states that a bipartite graph has a matching covering one side if and only if every subset has enough neighbors.
Hamiltonian cycle
A Hamiltonian cycle is a closed path in a graph that visits every vertex exactly once and returns to its start; it was posed as Hamilton's Icosian Game in 1857.