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Science Mathematics Discrete mathematics

Discrete mathematics

Addition principle

Counting principle in combinatorics

Adjacency matrix

Square matrix used to represent a graph or network

Algebraic combinatorics

Application of abstract algebra to combinatorics problems

Subset of incomparable elements

Antisymmetric relation

Binary relation such that if A is related to B and is different from it then B is not related to A

Bellman–Ford algorithm

Algorithm for finding the shortest paths in graphs

Formula used in graph theory

Binomial coefficient

Positive integers that occur as coefficients in the binomial theorem

Bipartite graph

Graph in which every vertex is connected to at least one other

Blossom algorithm

Algorithm for constructing maximum matchings on a graph

Boolean algebra (structure)

Algebraic structure modeling logical operations

Bridge (graph theory)

Edge in node-link graph whose removal would disconnect the graph

Cage (graph theory)

Regular graph that has as few vertices as possible for its girth

Graph whose vertices and edges represent the elements of a group and their products with the generators of the group

Chromatic polynomial

Polynomial defined from a node-link graph, that counts the number of graph colorings as a function of the number of colors

Circulation problem

Generalization of network flow problems

Clique (graph theory)

Subset of the vertices of a node-link graph that are all adjacent to each other

Computational problem of finding cliques in a graph

Selection of items from a collection

Combinatorial principles

Combinatorial methods used in combinatorics, a branch of mathematics

Branch of discrete mathematics

Mathematical relation with respect to a partial order

Graph in which every two vertices are adjacent

Component (graph theory)

Maximal subgraph of a given node-link graph within which every two vertices may be connected by a path

Connected relation

Binary endorelation such that for every pair of elements either first is related with second or second is related with first

Connectivity (graph theory)

Basic concept of graph theory

Covering relation

Mathematical relation inside orderings

Graph with 28 vertices and 42 edges

Crossing number (graph theory)

The smallest number of edge crossings possible in a drawing of a node-link graph

Crossing number inequality

Theorem providing a lower bound to the crossing number; for sufficiently large graphs, the crossing number is not less than a constant times the cube of the number of edges divided by the square of the number of vertices

Cycle (graph theory)

Trail in which the only repeated vertices are the first and last

Degree (graph theory)

Number of edges incident to a given vertex in a node-link graph

Type of matrix in algebraic graph theory

Dijkstra's algorithm

Algorithm for finding shortest paths

Graph with oriented edges

Discrete mathematics

Study of discrete mathematical structures

Branch of mathematics relating to posets

Double counting (proof technique)

Type of proof technique

Duality (order theory)

Term in the mathematical area of order theory

Undirected graph

Edge contraction

Operation that removes an edge from a graph and combines its endpoints into a single vertex

A set of edges that touches every vertex of a graph

Enumerative combinatorics

Area of combinatorics that deals with the number of ways certain patterns can be formed

Trail in a finite graph which visits every edge exactly once

Filter (mathematics)

In mathematics, a special subset of a partially ordered set

Algorithm for counting perfect matchings in planar graphs

Directed graph where each edge has a capacity and each edge receives a flow

Floyd–Warshall algorithm

Algorithm for finding all-pairs shortest paths in graphs, allowing some edge weights to be negative

Ford–Fulkerson algorithm

Algorithm to compute the maximum flow in a flow network (equivalently; the minimum cut)

Four color theorem

Statement in mathematics

Directed graph where edge-directions are labeled using group elements

Gale–Shapley algorithm

Algorithm for solving the stable matching problem

Generalized Petersen graph

Family of cubic graphs formed from regular and star polygons

Girth (graph theory)

Length of a shortest cycle contained in the graph

Graph (discrete mathematics)

Mathematical structure consisting of vertices and edges connecting some pairs of vertices

Graph automorphism

Symmetry of a graph onto itself preserving the edge–vertex connectivity

Methodic assignment of colors to elements of a graph

Graph homomorphism

A structure-preserving correspondence between node-link graphs

Graph isomorphism

Bijection between the vertex set of two graphs

Graph isomorphism problem

Unsolved problem in computational complexity theory

Graph formed from another graph by deleting edges and vertices and contracting edges

Area of discrete mathematics

Greatest element and least element

An element of a preordered set that is ≥ (respectively, ≤) to all other elements (in contrast, it is maximal if it is the only element ≥ to itself)

Hamiltonian path

Path in a graph that visits each vertex exactly once

Hamiltonian path problem

Problem of finding a cycle through all vertices of a graph

Handshaking lemma

Lemma that every node-link graph has an even number of odd-degree vertices

Visual depiction of a partially ordered set

Held–Karp algorithm

Solution of the traveling salesman problem

Bipartite undirected graph

Homeomorphism (graph theory)

Concept in graph theory

Hopcroft–Karp algorithm

Algorithm for maximum cardinality matching in bipartite graphs

Number of matchings in a graph

Generalization of graph theory

Ideal (order theory)

In order theory, a nonempty, upward‐directed, downward‐closed subset of a preordered set

Inclusion–exclusion principle

Counting technique in combinatorics

Infimum and supremum

Greatest lower bound and least upper bound

Intersection graph

Non-oriented graph in which two nodes are linked if and only if the two parts of a common space and represented by these nodes have a non-empty intersection in that space

Two related operations on a poset in order theory

Kőnig's theorem (graph theory)

Theorem showing that maximum matching and minimum vertex cover are equivalent for bipartite graphs

Kruskal's algorithm

Minimum spanning forest algorithm that greedily adds edges

Kuratowski's theorem

Theorem characterizing planar graphs

Mathematical sequence

Laplacian matrix

Matrix representation of a graph

Square array with symbols that each occur once per row and column

Lattice (order)

Set whose pairs have minima and maxima

Concept in graph theory

Lovász conjecture

Unproven conjecture, that every finite connected vertex-transitive graph contains a Hamiltonian path

Matching (graph theory)

Set of edges without common vertices

Matching polynomial

Graph polynomial generating numbers of matchings

Max-flow min-cut theorem

Concept in optimization theory

Maximum cardinality matching

A graph theory problem

Maximum flow problem

Computational problem in graph theory

Method of distinguished element

Method in enumerative combinatorics

Minimum-cost flow problem

Mathematical optimization problem

Multi-commodity flow problem

Flow network problem with multiple commodities between different source and sink nodes

Undirected graph which is permitted to have multiple edges but no loops

Mutually orthogonal Latin squares

Mathematical problem

Nowhere-zero flow

Concept in graph theory

Branch of mathematics

Partial permutation

Selection of some objects in a particular order

Partially ordered set

Mathematical set with an ordering

Pascal's triangle

Triangular array of the binomial coefficients in mathematics

Path (graph theory)

Sequence of edges connecting a sequence of vertices in a graph, with no repeating vertices

Perfect matching

Graph theory term

Change of ordering in a (mathematical) set

Cubic graph with 10 vertices and 15 edges

Pigeonhole principle

If there are more items than boxes holding them, one box must contain at least two items

Graph that can be embedded in the plane

Technique for drawing non-planar graphs

Reflexive and transitive binary relation

Prim's algorithm

Push–relabel maximum flow algorithm

Rainbow matching

Edge-colored graph matching where all edges have distinct colors

Branch of mathematics that studies the conditions under which order must appear

Where each vertex has the same number of neighbors

Rule of division (combinatorics)

Counting principle

Rule of product

Combinatorial principle to determine possible ways to match disjoint sets.

Seven Bridges of Königsberg

Classic problem in graph theory

Shortest path problem

Computational problem of graph theory

Snark (graph theory)

Bridgeless cubic graph with chromatic index equal to 4

Spectral graph theory

Linear algebra aspects of graph theory

Stable matching problem

Pairing where no unchosen pair prefers each other over their choice

Stable roommates problem

Mathematical problem of finding a stable matching for an even-sized set

Stirling number

Important sequences in combinatorics

Stirling numbers of the first kind

Numbers important in combinatorics

Stirling numbers of the second kind

Numbers parameterizing ways to partition a set

Tait's conjecture

Disproven graph theory

Three utilities problem

Mathematical puzzle of avoiding crossings

Mathematical ordering where all elements can be compared

Travelling salesman problem

NP-hard problem in combinatorial optimization

Tree (graph theory)

Undirected, connected and acyclic graph

Turán's brick factory problem

Problem of minimizing crossings in complete bipartite graphs

Tutte–Berge formula

A characterization of the size of a maximum matching in a graph

Systematic classification of 12 related enumerative problems concerning two finite sets

Maximal proper filter

Upper and lower bounds

Majorant and minorant in mathematics

Subset of a graph's vertices, including at least one endpoint of every edge

Vizing's theorem

A theorem in graph coloring

Well-founded relation

Type of binary relation

Class of mathematical orderings