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Undirected graph
In graph theory, a critical graph is an undirected graph all of whose proper subgraphs have smaller chromatic number. In such a graph, every vertex or
Critical_graph
Graph of n vertices with a perfect matching for every subgraph of n-1 vertices
In graph theory, a mathematical discipline, a factor-critical graph (or hypomatchable graph) is a graph with an odd number of vertices in which deleting
Factor-critical_graph
Operation that combines two graphs
In graph theory, the join operation is a graph operation that combines two graphs by connecting every vertex of one graph to every vertex of the other
Join_(graph_theory)
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes
Glossary_of_graph_theory
Graph operation
construct any critical graph or any graph whose chromatic number is at least some given threshold. Let G and H be two undirected graphs, vw be an edge
Hajós_construction
Maximal subgraph whose vertices can reach each other
In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph
Component_(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
Partition of graph into sequence of paths
In graph theory, an ear of an undirected graph G is a path P where the two endpoints of the path may coincide, but where otherwise no repetition of edges
Ear_decomposition
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
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
Graph of triangles with a shared vertex
the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and
Friendship_graph
Point where the derivative of a function is zero or undefined (in certain cases)
A critical value is the image under f of a critical point. These concepts may be visualized through the graph of f: at a critical point, the graph has
Critical_point_(mathematics)
American mathematician
including work on Brooks' theorem, the Borodin–Kostochka conjecture, list critical graphs, and Read's conjecture. Rabern earned a Ph.D. in mathematics from Arizona
Landon_Rabern
Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De
List_of_graph_theory_topics
Polynomial function of degree 3
have at least one real root. The graph of a cubic function always has a single inflection point. It may have two critical points, a local minimum and a local
Cubic_function
Mathematical theory on behavior of connected clusters in a random graph
complete graphs is an example of a random graph. The critical probability is p = 1/N, where N is the number of vertices (sites) of the graph. Bootstrap
Percolation_theory
Two closely related models for generating random graphs
the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
Derived graph of higher chromatic number
In the mathematical area of graph theory, the Mycielskian or Mycielski graph of an undirected graph is a larger graph formed from it by a construction
Mycielskian
Graph that misrepresents data
In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the
Misleading_graph
Representation of a mathematical function
In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle
Graph_of_a_function
Graph with equal-size maximal independent sets
In graph theory, a well-covered graph is an undirected graph in which the minimal vertex covers all have the same size. Here, a vertex cover is a set
Well-covered_graph
Mathematical abstraction of level sets
equivalent to a finite graph. In particular, the Reeb graph of a smooth function on a closed manifold with a finite number of critical values –which is the
Reeb_graph
Unsolved problem on graph coloring
needed to color biplanar graphs? More unsolved problems in mathematics The Earth–Moon problem is an unsolved problem on graph coloring in mathematics.
Earth–Moon_problem
Type of diagrammatic notation for propositional logic
An existential graph is a type of diagrammatic or visual notation for logical expressions, created by Charles Sanders Peirce, who wrote on graphical logic
Existential_graph
Smallest amount of fissile material needed to sustain a nuclear reaction
engineering, critical mass is the minimum mass of the fissile material needed for a sustained nuclear chain reaction in a particular setup. The critical mass
Critical_mass
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)
Cryptocurrency
The Graph is an open-source, decentralized protocol that powers the indexing and querying of blockchain data. It enables developers to build scalable
The_Graph
Critical point on a surface graph which is not a local extremum
point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not
Saddle_point
Graphical representation of a computer program or algorithm
In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a function during
Control-flow_graph
combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
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
Large connected component of a random graph
component of a given random graph that contains a significant fraction of the entire graph's vertices. More precisely, in graphs drawn randomly from a probability
Giant_component
Subgraph with contracted edges
In graph theory, an undirected graph H is called a minor of the undirected graph G if H can be formed from G by deleting edges and vertices and by contracting
Graph_minor
Creating a new graph from an existing graph
computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It
Graph_rewriting
Assignment of colors to edges of a graph
In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color
Edge_coloring
Geometry problem on tiling by hypercubes
reformulation of the problem in terms of the clique number of certain graphs now known as Keller graphs. The related Minkowski lattice cube-tiling conjecture states
Keller's_conjecture
On coloring the edges of graphs
In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than
Vizing's_theorem
French mathematician
mathematician known for her research in graph theory, including work on well-covered graphs, factor-critical graphs, spectral graph theory, Hamiltonian decomposition
Odile_Favaron
Mathematical parameter in percolation theory
percolation, a percolation transition is characterized by a set of universal critical exponents, which describe the fractal properties of the percolating medium
Percolation critical exponents
Percolation_critical_exponents
Problem of finding the longest simple path for a given graph
linear time solution for directed acyclic graphs, which has important applications in finding the critical path in scheduling problems. The NP-hardness
Longest_path_problem
Formula to quantify column buckling under a given load
column material and the critical stress given by Euler's formula. It creates a new failure border by fitting a parabola to the graph of failure for Euler
Johnson's_parabolic_formula
Graph drawing used to study Riemann surfaces
In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann surfaces and to provide combinatorial invariants for the action of
Dessin_d'enfant
Measurement of graph sparsity
In graph theory, a k-degenerate graph is an undirected graph in which every non-empty subgraph has at least one vertex of degree at most k {\displaystyle
Degeneracy_(graph_theory)
Graph database implemented in Java
global graph intelligence company that provides technology for analyzing and managing connected data. It is most known for creating the Neo4j Graph database
Neo4j
Refrigerant fluid
Rapid growth of R-410A (HFC-125/HFC-32) atmospheric concentrations, when & IF leaked (bottom-right graph).
R-410A
Graph made from a subset of another graph's nodes and their edges
In graph theory, an induced subgraph of a graph is another graph, formed from a subset of the vertices of the graph and all of the edges, from the original
Induced_subgraph
Intersection graph for curves in the plane
graph theory, a string graph is an intersection graph of curves in the plane; each curve is called a "string". Given a graph G, G is a string graph if
String_graph
Parameter describing physics near critical points
exponents Percolation critical exponents Network science Percolation theory Graph theory Hagen Kleinert and Verena Schulte-Frohlinde, Critical Properties of φ4-Theories
Critical_exponent
Type of graph with a sharp turn
A hockey stick graph or hockey stick curve is a graph, or curve shape, that resembles an ice hockey stick, in that it turns sharply from a nearly flat
Hockey_stick_graph
Node ordering for directed acyclic graphs
computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u
Topological_sorting
Protected section of code that cannot be executed by more than one process at a time
avoid the concurrent access. One way to do so is known as a critical section or critical region. This protected section cannot be entered by more than
Critical_section
Academic field
foundation of graph theory, a branch of mathematics that studies the properties of pairwise relations in a network structure. The field of graph theory continued
Network_science
Graph being ported This graph is being converted from the old graph extension to the new chart extension.
Opinion polling on the Narendra Modi premiership
Opinion_polling_on_the_Narendra_Modi_premiership
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
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)
Partition of the vertices of a graph
In graph theory, the Gallai–Edmonds decomposition is a partition of the vertices of a graph into three subsets which provides information on the structure
Gallai–Edmonds_decomposition
Philosophical model of the connections present in an assemblage
Mutualism Perspectivism Plane of immanence Graph (abstract data type) Arborescence (graph theory) Tree (graph theory) Digital infinity Intertwingularity
Rhizome_(philosophy)
When every path in a control-flow graph must go through one node to reach another
In computer science, a node d of a control-flow graph dominates a node n if every path from the entry node to n must go through d. Notationally, this
Dominator_(graph_theory)
is complete (see complete graph). A random network is in a supercritical regime if the average degree exceeds the critical point, that is if ⟨ k ⟩ > 1
Critical point (network science)
Critical_point_(network_science)
Relation between graph coloring and crossings
Unsolved problem in mathematics Do complete graphs have the smallest possible crossing number among graphs with the same chromatic number? More unsolved
Albertson_conjecture
Method of planning and managing projects
Critical chain project management (CCPM) is a method of planning and managing projects that emphasizes the resources (people, equipment, physical space)
Critical chain project management
Critical_chain_project_management
Type of graph in mathematics
specifically in graph theory, a polytree (also called directed tree, oriented tree or singly connected network) is a directed acyclic graph whose underlying
Polytree
Hungarian mathematician (1931–2023)
February 1931 – 6 June 2023) was a Hungarian mathematician. The Andrásfai graph was named after him. Andrásfai began his high school studies in 1942 at
Béla_Andrásfai
Cellular automaton
trees of the graph. The original interest behind the model stemmed from the fact that in simulations on lattices, it is attracted to its critical state, at
Abelian_sandpile_model
Representation of a graph as a path graph "thickened" by some amount
In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number
Pathwidth
Hungarian set theorist
on the number of edges in a critical graph for domination. A paper with Erdős on graph coloring problems for infinite graphs and hypergraphs. This paper
András_Hajnal
Graph whose line graph is perfect
In graph theory, a line perfect graph is a graph whose line graph is a perfect graph. Equivalently, these are the graphs in which every odd-length simple
Line_perfect_graph
Conjecture in graph theory
problem in mathematics Are graphs uniquely determined by their subgraphs? More unsolved problems in mathematics In graph theory, informally, the reconstruction
Reconstruction_conjecture
Polynomial equation of degree 3
corrects for scale. For the non-depressed case (1) (shown in the accompanying graph), the depressed case as indicated previously is obtained by defining t such
Cubic_equation
Type of random graph
cluster model has a critical limit, described by a conformal field theory. Let G = ( V , E ) {\displaystyle G=(V,E)} be a graph, and ω : E → { 0 , 1
Random_cluster_model
2018 mathematics text
so-called critical states, form an abelian group under this addition operation. The abelian sandpile model applies this model to large grid graphs, with the
The Mathematics of Chip-Firing
The_Mathematics_of_Chip-Firing
Planar maps require at most four colors
terms of graph theory, by considering it in terms of constructing a graph coloring of the planar graph of adjacencies between regions. In graph-theoretic
Four_color_theorem
Concept in physics
Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays
Self-organized_criticality
Threshold of percolation theory models
random systems or networks (graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation probability
Percolation_threshold
Cost accounting model
contribution = fixed costs. Mathematically, the contribution graph is obtained from the sales graph by a shear, to be precise ( 1 0 − V 1 ) {\displaystyle
Cost–volume–profit_analysis
Hungarian mathematics teacher
after György Hajós (1961), that may be used to construct any critical graph or any graph whose chromatic number is at least some given threshold. He earned
László_Rátz
List of Windows 10 operating system versions
environments to receive non-critical updates at a slower pace or use long-term support milestones that will only receive critical updates, such as security
Windows_10_version_history
Social structure made up of a set of social actors
field which emerged from social psychology, sociology, statistics, and graph theory. Georg Simmel authored early structural theories in sociology emphasizing
Social_network
Index of articles associated with the same name
undirected graphs Elimination ordering of chordal graphs Order, the complexity of a structure within a graph: see haven (graph theory) and bramble (graph theory)
Order_(mathematics)
Indian film director, producer, writer
Imtiaz Ali, Beg co-wrote the 2011 film Rockstar which earned him wide critical reception and Zee Cine Award 2011. In 2012, Beg came up with his directorial
Muazzam_Beg
Topological index of a molecule
In chemical graph theory, the Wiener index (also Wiener number) introduced by Harry Wiener, is a topological index of a molecule, defined as the sum of
Wiener_index
Analysis of social structures using network and graph theory
process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of nodes (individual
Social_network_analysis
Conjecture on zeros of the zeta function
the two-by-two p-adic special linear group. A regular finite graph is a Ramanujan graph, a mathematical model of efficient communication networks, if
Riemann_hypothesis
Point where the curvature of a curve changes sign
at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave
Inflection_point
Swiss mathematician (1707–1783)
his studies of beam bending and column critical loads. Euler is credited with being the first to develop graph theory (partly as a solution for the problem
Leonhard_Euler
Graph invariant measuring irregularity
irregularity or Albertson irregularity index) is a graph invariant that measures the irregularity of a graph by summing the imbalances of all its edges. It
Albertson_index
Cosmological fine-tuning problem
specific critical value being required for a flat universe. The current density of the universe is observed to be very close to this critical value. Since
Flatness_problem
Curve for failure rates over time
curve is a failure rate graph that curves up at both ends, similar in shape to a bathtub. The term can also apply to any graph with this shape. Many but
Bathtub_curve
State of matter
dynamics and long-range correlations. This transition to BEC occurs below a critical temperature, which for a uniform three-dimensional gas consisting of non-interacting
Bose–Einstein_condensate
Analysis of social relationships in terms of network theory
structuring a criminal network." It revealed "a minority of these actors were critical to the network in two ways: (1) they were active in bringing other participants
Social network analysis in criminology
Social_network_analysis_in_criminology
Problem of determining if a Boolean formula could be made true
answers. For example, deciding whether a given graph has a 3-coloring is another problem in NP; if a graph has 17 valid 3-colorings, then the SAT formula
Boolean satisfiability problem
Boolean_satisfiability_problem
Process of generalization
they are not abstract in the sense of the objects in graph 1 below. We might look at other graphs, in a progression from cat to mammal to animal, and see
Abstraction
Mathematical function, inverse of an exponential function
shown at the right: a point (t, u = bt) on the graph of f yields a point (u, t = logb u) on the graph of the logarithm and vice versa. As a consequence
Logarithm
A Graph Coarsening Algorithm is a family of metaheuristic algorithms used to reduce the size and complexity of a large graph while preserving its key structural
Graph_Coarsening_Algorithm
Study of rates of change
Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is
Differential_calculus
Randomized algorithm for minimum cuts
In computer science and graph theory, Karger's algorithm is a randomized algorithm to compute a minimum cut of a connected graph. It was invented by David
Karger's_algorithm
Game in structural combinatorics
The chip-firing game is a one-player game on a graph which was invented around 1983 and since has become an important part of the study of structural
Chip-firing_game
graph comprehension. Spatial Cognition & Computation, 12, 1–25 Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors
Graph_literacy
Network whose degree distribution follows a power law
transformation which converts random graphs to their edge-dual graphs (or line graphs) produces an ensemble of graphs with nearly the same degree distribution
Scale-free_network
with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory
List of atheists in science and technology
List_of_atheists_in_science_and_technology
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