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Set of edges without common vertices
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In
Matching_(graph_theory)
Problem of finding similarity between graphs
Graph matching is the problem of finding a similarity between graphs. Graphs are commonly used to encode structural information in many fields, including
Graph_matching
On bipartite matching and vertex cover
mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem and the minimum
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Matching which covers every node of the graph
In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. More formally, given a graph G with edges E and vertices
Perfect_matching
Unsolved problem in computational complexity theory
known as the exact graph matching problem. In November 2015, László Babai announced a quasi-polynomial time algorithm for all graphs, that is, one with
Graph_isomorphism_problem
Graph theory problem: find a matching containing the most edges
In graph theory, a maximum-cardinality matching is a special kind of subgraph useful in many computational contexts. Given a graph G, a matching is a
Maximum-cardinality_matching
Graph theory problem
Maximum-weight matching is an optimization problem in graph theory in which the goal is to find a matching of maximum possible total weight in an edge-weighted
Maximum-weight_matching
Set of hyperedges where every pair is disjoint
In graph theory, a matching in a hypergraph is a set of hyperedges, in which every two hyperedges are disjoint. It is an extension of the notion of matching
Matching_in_hypergraphs
Graph polynomial generating numbers of matchings
graph theory and combinatorics, a matching polynomial (sometimes called an acyclic polynomial) is a generating function of the numbers of matchings of
Matching_polynomial
Graph divided into two independent sets
bipartite graphs are the crown graphs, formed from complete bipartite graphs by removing the edges of a perfect matching. Hypercube graphs, partial cubes
Bipartite_graph
graph theory, an induced matching or strong matching is a subset of the edges of an undirected graph that do not share any vertices (it is a matching)
Induced_matching
the line graph instead of the given graph. For instance, α(G) is the independence number of a graph; α′(G) is the matching number of the graph, which equals
Glossary_of_graph_theory
Shape representing matchings in a graph
In graph theory, the matching polytope of a given graph is a geometric object representing the possible matchings in the graph. It is a convex polytope
Matching_polytope
Partition of a graph into spanning subgraphs
graph into disjoint k-factors. A graph G is said to be k-factorable if it admits a k-factorization. In particular, a 1-factor is a perfect matching,
Graph_factorization
Algorithm for finding max graph matchings
In graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. The algorithm was developed by Jack Edmonds in 1961
Blossom_algorithm
Characterization of graphs with perfect matchings
discipline of graph theory, the Tutte theorem, named after William Thomas Tutte, is a characterization of finite undirected graphs with perfect matchings. It is
Tutte's theorem on perfect matchings
Tutte's_theorem_on_perfect_matchings
Graph of n vertices with a perfect matching for every subgraph of n-1 vertices
results in a graph with a perfect matching, a way of grouping the remaining vertices into adjacent pairs. A matching of all but one vertex of a graph is called
Factor-critical_graph
Largest independent set of paired elements
(1976) as a common generalization of graph matching and matroid intersection. It is also known as polymatroid matching, or the matchoid problem. Matroid
Matroid_parity_problem
Topics referred to by the same term
Look up matching in Wiktionary, the free dictionary. Matching may refer to: Matching, Essex, England Matching Green Matching Tye Matching (graph theory)
Matching
Result in combinatorics and graph theory
number of sets in the subset. The graph theoretic formulation answers whether a finite bipartite graph has a perfect matching—that is, a way to match each
Hall's_marriage_theorem
Creating a new graph from an existing graph
rewrite rule is applied to the host graph by searching for an occurrence of the pattern graph (pattern matching, thus solving the subgraph isomorphism
Graph_rewriting
Cubic graph with 10 vertices and 15 edges
bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the
Petersen_graph
Graphs formed by a hypercube's edges and vertices
complete graph, and may be decomposed into two copies of Q n − 1 {\displaystyle Q_{n-1}} connected to each other by a perfect matching. Hypercube graphs should
Hypercube_graph
Measure of similarity between two graphs
application of graph edit distance is in inexact graph matching, such as error-tolerant pattern recognition in machine learning. The graph edit distance
Graph_edit_distance
Topics referred to by the same term
matchings. Matching (graph theory) - a mathematical theory studying the properties and computation of matchings in networks (graphs). This disambiguation
Matching_theory
Query language for property graphs
property graph may have a set of labels and a set of properties that are associated with the graph as a whole. GQL queries operate by pattern matching over
Graph_Query_Language
In graph theory, a fractional matching is a generalization of a matching in which, intuitively, each vertex may be broken into fractions that are matched
Fractional_matching
Problem of grouping into triples
mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (also known as 2-dimensional matching) to 3-partite hypergraphs
3-dimensional_matching
Edge-colored graph matching where all edges have distinct colors
of graph theory, a rainbow matching in an edge-colored graph is a matching in which all the edges have distinct colors. Given an edge-colored graph G =
Rainbow_matching
Database using graph structures for queries
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key
Graph_database
Algorithm for maximum cardinality matching
algorithm) is an algorithm that takes a bipartite graph as input and produces a maximum-cardinality matching as output — a set of as many edges as possible
Hopcroft–Karp_algorithm
Graph representing edges of another graph
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges
Line_graph
Functional programming construct
Pattern language — metaphoric, drawn from architecture Graph matching Two-dimensional pattern matching The Mathematica Book, chapter Section 2.3: Patterns
Pattern_matching
Technique in computer science
Semantic matching is a technique used in computer science to identify information that is semantically related. Given any two graph-like structures, e
Semantic_matching
Robustness of graph perfect matchings
In graph theory, a branch of mathematics, the matching preclusion number of a graph G {\displaystyle G} , denoted m p ( G ) {\displaystyle \mathrm {mp}
Matching_preclusion
Type of graph in mathematics and physics
functions on the edges of the graph and specifying matching conditions at the vertices. The trivial example of matching conditions that make the operator
Quantum_graph
Combinatorial optimization problem
describing the problem using graph theory: The assignment problem consists of finding, in a weighted bipartite graph, a matching of maximum size, in which
Assignment_problem
Bipartite graph where each node of 1st set is linked to all nodes of 2nd set
class of sparse graphs defined by avoidance of complete bipartite subgraphs Crown graph, a graph formed by removing a perfect matching from a complete
Complete_bipartite_graph
On chains and antichains in partial orders
combinatorics, Dilworth's theorem is equivalent to Kőnig's theorem on bipartite graph matching and several other related theorems including Hall's marriage theorem
Dilworth's_theorem
Geometric graph with unit edge lengths
In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting
Unit_distance_graph
Undirected graph with 14 vertices
distance-transitive graph (see the Foster census) and therefore distance regular. There are 24 perfect matchings in the Heawood graph; for each matching, the set
Heawood_graph
Graph without four-vertex star subgraphs
order have perfect matchings, the discovery of polynomial time algorithms for finding maximum independent sets in claw-free graphs, and the characterization
Claw-free_graph
Mathematical graph theorem
Petersen's Theorem. Every cubic, bridgeless graph contains a perfect matching. In other words, if a graph has exactly three edges at each vertex, and
Petersen's_theorem
Pairing where no unchosen pair prefers each other over their choice
Envy-free matching – a relaxation of stable matching for many-to-one matching problems Rainbow matching for edge colored graphs Stable matching polytope
Stable_matching_problem
number of edges in a balanced bipartite graph whose edges can be partitioned into a linear number of induced matchings, or the maximum number of triples one
Ruzsa–Szemerédi_problem
Pattern recognition technique
Elastic matching is one of the pattern recognition techniques in computer science. Elastic matching (EM) is also known as deformable template, flexible
Elastic_matching
Branch of the mathematical field of graph theory
topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological
Topological_graph_theory
Index of articles associated with the same name
corresponding to certain closed walks in a graph. The Martin polynomial, used by Pierre Martin to study Euler tours The matching polynomials, several different polynomials
Graph_polynomial
In graph theory, Berge's theorem states that a matching M in a graph G is maximum (contains the largest possible number of edges) if and only if there
Berge's_theorem
Field of market economics
bipartite graph. The typical example is men and women, as in the campus Marriage Pact. Hospitals-residents problem - a one-to-many matching between agents
Matching_markets
Greek and American computer scientist
machine learning and data mining to graph-theoretic data, including the use of graph neural networks and graph matching, and applications to anomaly detection
Danai_Koutra
Acting President of Zambia from 2014 to 2015
paper” and remains a standard reference in point-pattern matching, spectral graph matching, point-set registration, and even medical/neuroimaging correspondence
Guy_Scott
Unrelated vertices in graphs
In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a
Independent set (graph theory)
Independent_set_(graph_theory)
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
Refinement of perfect matching theorems
Deficiency is a concept in graph theory that is used to refine various theorems related to perfect matching in graphs, such as Hall's marriage theorem
Deficiency_(graph_theory)
Characterization of the size of a maximum matching in a graph
mathematical discipline of graph theory the Tutte–Berge formula is a characterization of the size of a maximum matching in a graph. It is a generalization
Tutte–Berge_formula
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Graph data structure
preserve the e-graph invariants. The last operation, e-matching, is described below. An e-graph can also be formulated as a bipartite graph G = ( N ⊎ i d
E-graph
Directed graph isomorphic to its own transpose graph
finding matchings in graphs, in testing whether a still life pattern in Conway's Game of Life may be partitioned into simpler components, in graph drawing
Skew-symmetric_graph
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
Generalizations in graph theory
condition guaranteeing that a bipartite graph (X + Y, E) admits a perfect matching, or - more generally - a matching that saturates all vertices of Y. The
Hall-type theorems for hypergraphs
Hall-type_theorems_for_hypergraphs
Graph matching with max number of high-priority vertices
In graph theory, a priority matching (also called: maximum priority matching) is a matching that maximizes the number of high-priority vertices that participate
Priority_matching
Graph with tight clique-coloring relation
theorem on matchings, and the Erdős–Szekeres theorem on monotonic sequences, can be expressed in terms of the perfection of certain associated graphs. The perfect
Perfect_graph
British computer scientist (1956–2024)
performed using data in the form of graphs, trees and strings. He was best known for his work on graph matching and spectral graph theory. He also worked on physics
Edwin_Hancock
Data query language developed by Facebook
the GraphQL server will return data matching the shape defined by the mutation. { "data": { "createUser": { "name": "Han Solo", "age": 42 } } } GraphQL
GraphQL
Planar, undirected graph with 2n vertices and 3n-2 edges
mathematical field of graph theory, the ladder graph Ln is a planar, undirected graph with 2n vertices and 3n − 2 edges. The ladder graph can be obtained as
Ladder_graph
Searching for patterns in text
Clifford. Sequence alignment Graph matching Pattern matching Compressed pattern matching Matching wildcards Approximate string matching Full-text search Two-dimensional
String-searching_algorithm
each direction. When a graph has a Pfaffian orientation, the orientation can be used to count the perfect matchings of the graph. This is the main idea
Pfaffian_orientation
Graph of chess rook moves
In graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's
Rook's_graph
Graph generated by a random process
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability
Random_graph
Statistical matching technique
statistical analysis of observational data, propensity score matching (PSM) is a statistical matching technique that attempts to estimate the effect of a treatment
Propensity_score_matching
Technology capable of matching a face from an image against a database of faces
his research team at the University of Bochum developed Elastic Bunch Graph Matching in the mid-1990s to extract a face out of an image using skin segmentation
Facial_recognition_system
Geometric construct
unit squares meeting edge-to-edge. Equivalently, it is a perfect matching in the grid graph formed by placing a vertex at the center of each square of the
Domino_tiling
Subset of a graph's vertices, including at least one endpoint of every edge
in cubic graphs and even in planar graphs of degree at most 3. For bipartite graphs, the equivalence between vertex cover and maximum matching described
Vertex_cover
Graph with all vertices of degree 4
mathematical field of graph theory, a quartic graph is a graph where all vertices have degree 4. In other words, a quartic graph is a 4-regular graph. Several well-known
Quartic_graph
Non-crossing graph with vertices on outer face
planarity of graphs formed by using a perfect matching to connect two copies of a base graph (for instance, many of the generalized Petersen graphs are formed
Outerplanar_graph
009. Umeyama, S (1988). "An eigendecomposition approach to weighted graph matching problems". IEEE Transactions on Pattern Analysis and Machine Intelligence
Spectral_shape_analysis
In graph theory, a maximally matchable edge in a graph is an edge that is included in at least one maximum-cardinality matching in the graph. An alternative
Maximally_matchable_edge
Partition of the vertices of a graph
subsets which provides information on the structure of maximum matchings in the graph. Tibor Gallai and Jack Edmonds independently discovered it and proved
Gallai–Edmonds_decomposition
American computer scientist
environments. Other areas of interest include database tuning and tree and graph matching. After graduating from Yale in 1977, he worked for IBM designing circuits
Dennis_Shasha
Concept in natural language processing
a partially ordered set and represented as nodes of a directed acyclic graph (e.g., a taxonomy), would be the shortest-path linking the two concept nodes
Semantic_similarity
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
Assignment of colors to edges of a graph
the multigraph case. A matching in a graph G is a set of edges, no two of which are adjacent; a perfect matching is a matching that includes edges touching
Edge_coloring
Problem in theoretical computer science
electronic circuits. Subgraph matching is also a substep in graph rewriting (the most runtime-intensive), and thus offered by graph rewrite tools. The problem
Subgraph_isomorphism_problem
In graph theory, the Tutte matrix A of a graph G = (V, E) is a matrix used to determine the existence of a perfect matching: that is, a set of edges which
Tutte_matrix
Graph in which every two vertices are adjacent
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique
Complete_graph
Partition of a graph whose components are reachable from all vertices
In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly
Strongly_connected_component
complex of a graph G, denoted M(G), is an abstract simplicial complex of the matchings in G. It is the independence complex of the line graph of G. The (m
Independence_complex
Form of pattern recognition
as in face recognition. A graph matching algorithm will yield the optimal correspondence. Grammar induction String matching Hopcroft–Karp algorithm Structural
Syntactic_pattern_recognition
Bipartite graph partition with special property
perfect matching of the graph. It is named after A. L. Dulmage and Nathan Mendelsohn, who published it in 1958. A generalization to any graph is the Edmonds–Gallai
Dulmage–Mendelsohn decomposition
Dulmage–Mendelsohn_decomposition
Mathematical tree of cycles
property of remaining connected after the removal of a matching. The largest triangular cactus in any graph may be found in polynomial time using an algorithm
Cactus_graph
Graph where every edge is in one triangle
vertex) the rest of the graph looks like a perfect matching. Locally linear graphs have also been called locally matched graphs. More technically, the
Locally_linear_graph
Abstract data type in computer science
science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within
Graph_(abstract_data_type)
Subset of a graph's edges
In graph theory, an edge cover of a graph is a set of edges such that every vertex of the graph is an endpoint of at least one edge of the set. In computer
Edge_cover
String-searching algorithm
Alfred V. Aho and Margaret J. Corasick in 1975. It is a kind of dictionary-matching algorithm that locates elements of a finite set of strings (the "dictionary")
Aho–Corasick_algorithm
visualize what different stable matchings look like (refer to the graphs on the right). Consider two different stable matchings, A and B. Consider a doctor
Rural_hospitals_theorem
Graph with all vertices of degree 3
of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are
Cubic_graph
original graph to an unweighted graph, in which each agent is adjacent only to his highest-valued houses, and look for a perfect matching in this graph. When
House_allocation_problem
Fewest graph edges whose removal breaks all cycles
In graph theory, a branch of mathematics, the cyclomatic number, circuit rank, cycle rank, corank or nullity of an undirected graph is the minimum number
Cyclomatic_number
Python module
graph-tool is a Python module for manipulation and statistical analysis of graphs (AKA networks). The core data structures and algorithms of graph-tool
Graph-tool
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