Discrete mathematics
Topics in mathematicsStatisticsCalculus and analysisGeometryDiscrete mathematicsFoundationsBasicsAlgebraStatistics and probabilityApplied mathematicsFunctionsMathematicsTheoretical computer scienceFrom Lably lessonsNumber theoryOtherCounting and numbersGeometry and topologyApplied MathematicsGeneralAnalysisArithmeticProbability and statistics
A
- Abstract machineTheoretical computer used for defining a model of computation
- Addition principleCounting principle in combinatorics
- Adjacency matrixSquare matrix used to represent a graph or network
- Algebraic combinatoricsArea of combinatorics
- Algebraic number fieldFinite extension of the rationals
- Algebraic number theoryBranch of number theory
- Analytic number theoryExploring properties of the integers with complex analysis
- AntichainSubset of incomparable elements
- Antisymmetric relationType of binary relation
- Asymmetric relationBinary relation which never occurs in both directions
- AxiomStatement that is taken to be true
- Axiom of choiceAxiom of set theory
B
- Bellman–Ford algorithmAlgorithm for finding the shortest paths in graphs
- Binomial coefficientNumber of subsets of a given size
- Bipartite graphGraph divided into two independent sets
- Biregular graphIn graph-theoretic mathematics, a biregular graph or semiregular bipartite graph is a bipa
- Blossom algorithmAlgorithm for finding max graph matchings
- Boolean algebra (structure)Algebraic structure modeling logical operations
- Bridge (graph theory)Edge whose deletion would disconnect a graph
- Burali-Forti paradoxParadox in set theory
C
- Cage (graph theory)Regular graph with fewest possible nodes for its girth
- CardinalitySize of a set in mathematics
- Cayley graphGraph defined from a mathematical group
- Charles Jean de la Vallée PoussinCharles-Jean Étienne Gustave Nicolas, baron de la Vallée Poussin (French pronunciation: ;
- Chromatic polynomialFunction in algebraic graph theory
- Circulation problemThe circulation problem and its variants are a generalisation of network flow problems, wi
- Class field theoryBranch of algebraic number theory concerned with abelian extensions
- Clique (graph theory)Adjacent subset of an undirected graph
- Clique problemTask of computing complete subgraphs
- Coding theoryStudy of the properties of codes and their fitness
- Colin de Verdière graph invariantColin de Verdière's invariant is a graph parameter for any graph G, introduced by Yves Col
- CombinationSelection of items from a set
- Combinatorial principlesMethods used in combinatorics
- Combinatorial proofIn mathematics, the term combinatorial proof is often used to mean either of two types of
- CombinatoricsBranch of discrete mathematics
- Complete graphGraph in which every two vertices are adjacent
- Component (graph theory)Maximal subgraph whose vertices can reach each other
- Computability theoryStudy of computable functions and Turing degrees
- Computable functionMathematical function that can be computed by a program
- Computational complexity theoryInherent difficulty of computational problems
- Connected relationProperty of a relation on a set
- Connectivity (graph theory)Basic concept of graph theory
- Constructivism (philosophy of mathematics)Philosphical view that existence proofs must be constructive
- Controlled natural languageSubset of a natural language
- Covering relationIn mathematics, especially order theory, the covering relation of a partially ordered set
- Crossing number (graph theory)Fewest edge crossings in drawing of a graph
- Cubic graphIn the mathematical field of graph theory, a cubic graph is a graph in which all vertices
- Cycle (graph theory)Trail in which only the first and last vertices are equal
- Cycles and fixed pointsIn mathematics, the cycles of a permutation π of a finite set S correspond bijectively to
D
- Data compressionCompact encoding of digital data
- Data structureParticular way of storing and organizing data in a computer
- Degree (graph theory)Number of edges touching a vertex in a graph
- Degree matrixType of matrix in algebraic graph theory
- Dijkstra's algorithmAlgorithm for finding shortest paths
- Diophantine equationPolynomial equation whose integer solutions are sought
- Directed acyclic graphDirected graph with no directed cycles
- Directed graphGraph with oriented edges
- Disquisitiones Arithmeticae1798 textbook by Carl Friedrich Gauss
- Domain theoryBranch of mathematics relating to posets
- Double counting (proof technique)Type of proof technique
- Dürer graphIn the mathematical field of graph theory, the Dürer graph is an undirected graph with 12
E
- Edge contractionDeleting a graph edge and merging its nodes
- Edge coverSubset of a graph's edges
- Empty setMathematical set containing no elements
- Enumerative combinatoricsArea of combinatorics that deals with the number of ways certain patterns can be formed
- Equivalence relationMathematical concept for comparing objects
- Error detection and correctionReliable digital data delivery methods on unreliable channels
- Euclid's theoremInfinitely many prime numbers exist
- Eulerian pathTrail in a graph that visits each edge once
F
- Fermat's Last Theorem17th-century conjecture proved by Andrew Wiles in 1994
- Filter (mathematics)Special subset of a partially ordered set
- First-order logicType of logical system
- FKT algorithmAlgorithm for counting perfect matchings in planar graphs
- Flow networkDirected graph where edges have a capacity
- Floyd–Warshall algorithmAlgorithm in graph theory
- Forbidden graph characterizationDescribing a family of graphs by excluding certain (sub)graphs
- Ford–Fulkerson algorithmAlgorithm to compute the maximum flow in a network
- Formal languageSequence of words formed by specific rules
- Four color theoremPlanar maps require at most four colors
- Fundamental theorem of arithmeticIntegers have unique prime factorizations
G
- Gale–Shapley algorithmProcedure for finding a stable matching
- Generalized Petersen graphFamily of cubic graphs formed from regular and star polygons
- Giant componentIn network theory, a giant component is a connected component of a given random graph that
- Girth (graph theory)Length of a shortest cycle contained in the graph
- Gödel's incompleteness theoremsLimitative results in mathematical logic
- Graph (discrete mathematics)Vertices connected in pairs by edges
- Graph automorphismMapping a graph onto itself without changing edge-vertex connectivity
- Graph coloringMethodic assignment of colors to elements of a graph
- Graph embeddingEmbedding a graph in a topological space, often Euclidean
- Graph homomorphismStructure-preserving correspondence between node-link graphs
- Graph isomorphismBijection between the vertex set of two graphs
- Graph isomorphism problemUnsolved problem in computational complexity theory
- Graph labelingAssignment of labels to elements of a graph
- Graph minorSubgraph with contracted edges
- Graph theoryArea of discrete mathematics
- Greatest element and least elementConcept in mathematics
H
- Hamiltonian pathPath in a graph that visits each vertex exactly once
- Hamiltonian path problemProblem of finding a cycle through all vertices of a graph
- Handshaking lemmaEvery graph has evenly many odd vertices
- Hasse diagramVisual depiction of a partially ordered set
- Held–Karp algorithmSolution of the traveling salesman problem
- Hilbert's programAttempt to formalize all of mathematics, based on a finite set of axioms
- Homeomorphism (graph theory)Graphs that differ only by edge subdivision
- Homogeneous relationBinary relation over a set and itself
- Hosoya indexNumber of matchings in a graph
- HypergraphGeneralization of graph theory
I
- Ideal (order theory)Nonempty, upper-bounded, downward-closed subset
- Inclusion–exclusion principleCounting technique in combinatorics
- Infimum and supremumGreatest lower bound and least upper bound
- Intersection (set theory)Set of elements common to all of some sets
- Intersection graphGraph representing intersections between given sets
J
K
- Kőnig's theorem (graph theory)On bipartite matching and vertex cover
- Kronecker–Weber theoremIn algebraic number theory, it can be shown that every cyclotomic field is an abelian exte
- Kruskal's algorithmMinimum spanning forest algorithm that greedily adds edges
- Kuratowski's theoremOn forbidden subgraphs in planar graphs
L
- Lah numberMathematical sequence
- Laman graphIn graph theory, the Laman graphs are a family of sparse graphs describing the minimally r
- Laplacian matrixMatrix representation of a graph
- Latin squareSquare array with symbols that each occur once per row and column
- Lattice (order)Set whose pairs have minima and maxima
- Line graphGraph representing edges of another graph
- Line graph of a hypergraphIn graph theory, particularly in the theory of hypergraphs, the line graph of a hypergraph
- Logical matrixMatrix of binary truth values
M
- Matching (graph theory)Set of edges without common vertices
- Matching polynomialGraph polynomial generating numbers of matchings
- Mathematical inductionForm of mathematical proof
- Mathematical logicSubfield of mathematics
- Max-flow min-cut theoremEquivalence of optimization problems
- Maximal and minimal elementsIn mathematics, especially in order theory, a maximal element of a subset of some preorder
- Maximum flow problemComputational problem in graph theory
- Maximum-cardinality matchingGraph theory problem: find a matching containing the most edges
- Mealy machineIn the theory of computation, a Mealy machine is a finite-state machine whose output value
- MultigraphGraph with multiple edges between two vertices
- Mutually orthogonal Latin squaresMathematical problem
N
O
P
- P versus NP problemUnsolved problem in computer science
- Paradoxes of set theoryThis article contains a discussion of paradoxes of set theory. As with most mathematical p
- Parameterized complexityIn computer science, parameterized complexity is a branch of computational complexity theo
- Partial permutationSelection in a particular order
- Partially ordered setMathematical set with an ordering
- Pascal's triangleTriangular array of the binomial coefficients
- Path (graph theory)Sequence of edges which join a sequence of vertices on a given graph
- PermutationMathematical version of an order change
- Petersen graphCubic graph with 10 vertices and 15 edges
- Pigeonhole principleTheorem in combinatorics
- Planar graphGraph that can be embedded in the plane
- PolytreeIn mathematics, and more specifically in graph theory, a polytree (also called directed tr
- Pre-orderA pre-order is an order placed for an item that has not yet been released. The idea for pr
- PreorderReflexive and transitive binary relation
- PrewellorderingSet theory concept
- Prim's algorithmMethod for finding minimum spanning trees
- Prime number theoremCharacterization of how many integers are prime
- Propositional logicBranch of logic
- Push–relabel maximum flow algorithmAlgorithm in mathematical optimization
R
- Ramsey theoryBranch of mathematical combinatorics
- Ramsey's theoremStatement in mathematical combinatorics
- Reduction (computability theory)In computability theory, many reducibility relations (also called reductions, reducibiliti
- Regular graphGraph where each vertex has the same number of neighbors
- Riemann hypothesisConjecture on zeros of the zeta function
- Rotation systemIn combinatorial mathematics, rotation systems (also called combinatorial embeddings or co
- Rule of productBasic counting principle in mathematics
- Russell's paradoxParadox in set theory
S
- Set theoryBranch of mathematics that studies sets
- Seven Bridges of KönigsbergClassic problem in graph theory
- Shortest path problemComputational problem of graph theory
- Skew-symmetric graphIn graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that
- Snark (graph theory)3-regular graph with no 3-edge-coloring
- Spectral graph theoryLinear algebra aspects of graph theory
- Stable matching problemPairing where no unchosen pair prefers each other over their choice
- Stable roommates problemType of stable matching problem
- Stirling numberMathematical sequences in combinatorics
- Stirling numbers of the first kindCount of permutations by cycles
- Stirling numbers of the second kindNumbers parameterizing ways to partition a set
- SubsetSet whose elements all belong to another set
- Symmetric differenceIn mathematics, the symmetric difference of two sets, also known as the disjunctive union
- Szpiro's conjectureIn number theory, Szpiro's conjecture relates to the conductor and the discriminant of an
T
- Tarski's undefinability theoremTarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an importa
- Ternary plotBarycentric plot on three variables
- Theoretical computer scienceSubfield of computer science and mathematics
- Theoretical Computer Science (journal)Theoretical Computer Science (TCS) is a computer science journal published by Elsevier, st
- Theory of computationAcademic subfield of computer science
- Thomas KirkmanThomas Penyngton Kirkman FRS (31 March 1806 – 3 February 1895) was a British mathematician
- Three utilities problemMathematical puzzle of avoiding crossings
- Total orderOrder whose elements are all comparable
- Travelling salesman problemNP-hard problem in combinatorial optimization
- Tree (descriptive set theory)In descriptive set theory, a tree on a set is a collection of finite sequences of elements
- Tree (graph theory)Undirected, connected, and acyclic graph
- Tree (set theory)Partial order with well-ordered predecessors
- Triangle-free graphIn the mathematical area of graph theory, a triangle-free graph is an undirected graph in
- Triangular arrayNumbers arranged in a triangle
- Turán's brick factory problemIn the mathematics of graph drawing, Turán's brick factory problem asks for the minimum nu
- Twelvefold waySystematic classification of 12 related enumerative problems concerning two finite sets
U
V
W
- Weak orderingMathematical ranking of a set
- Well-founded relationType of binary relation
- Well-orderClass of mathematical orderings
- Well-quasi-orderingMathematical concept for comparing objects
- Wiles's proof of Fermat's Last Theorem1995 publication in mathematics
- Wolfgang HakenWolfgang Haken (German: ; June 21, 1928 – October 2, 2022) was a German American mathemati