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In graph theory, a subfield of mathematics, a well-colored graph is an undirected graph for which greedy coloring uses the same number of colors regardless
Well-colored_graph
Maximum number of colors in a greedy graph coloring
whether a graph is well-colored is coNP-complete. The hereditarily well-colored graphs (graphs for which every induced subgraph is well-colored) are exactly
Grundy_number
vertex-weighted graph has weights on its vertices and an edge-weighted graph has weights on its edges. well-colored A well-colored graph is a graph all of whose
Glossary_of_graph_theory
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
One-by-one assignment of colors to graph vertices
number of colors that can be found by a greedy coloring), and the well-colored graphs, graphs for which all greedy colorings use the same number of colors
Greedy_coloring
Planar maps require at most four colors
graph can be colored with at most four colors so that no two adjacent vertices receive the same color, or for short: every planar graph is four-colorable
Four_color_theorem
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 formed by complementation and disjoint union
hereditarily well-colored graph, a graph such that every greedy coloring of every induced subgraph uses an optimal number of colors. A graph is a cograph
Cograph
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
Conjecture in graph theory
number of an undirected finite graph G {\displaystyle G} . The inequality χ(G × H) ≤ min {χ(G), χ(H)} is easy: if G is k-colored, one can k-color G × H by
Hedetniemi's_conjecture
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
Bijection between the vertex set of two graphs
labeled graphs, colored graphs, rooted trees and so on. The isomorphism relation may also be defined for all these generalizations of graphs: the isomorphism
Graph_isomorphism
In graph theory, a graph amalgamation is a relationship between two graphs (one graph is an amalgamation of another). Similar relationships include subgraphs
Graph_amalgamation
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
Unsolved problem in computational complexity theory
multiplicity k-Contractible graphs (a generalization of bounded degree and bounded genus) Color-preserving isomorphism of colored graphs with bounded color multiplicity
Graph_isomorphism_problem
Graph property
have invariant 1, and can be 2-colored; the outerplanar graphs have invariant two, and can be 3-colored; the planar graphs have invariant 3, and (by the
Colin de Verdière graph invariant
Colin_de_Verdière_graph_invariant
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
On coloring infinite graphs
that, when all finite subgraphs can be colored with c {\displaystyle c} colors, the same is true for the whole graph. The theorem was proved by Nicolaas
De Bruijn–Erdős theorem (graph theory)
De_Bruijn–Erdős_theorem_(graph_theory)
Graph colouring algorithm by Daniel Brélaz
Consider the graph G = ( V , E ) {\displaystyle G=(V,E)} shown on the right. This is a wheel graph and will therefore be optimally colored by the DSatur
DSatur
Pattern of states and moves in the Tower of Hanoi puzzle
In graph theory and recreational mathematics, the Hanoi graphs are undirected graphs whose vertices represent the possible states of the Tower of Hanoi
Hanoi_graph
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
3-regular graph with no 3-edge-coloring
mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three colors
Snark_(graph_theory)
Flow graph invented by Claude Shannon
Thus, signal-flow graph theory builds on that of directed graphs (also called digraphs), which includes as well that of oriented graphs. This mathematical
Signal-flow_graph
Knowledge base and note-taking software
traditional Markdown links. Links appear in Obsidian's interactive graph view. The graph view is a visualization of notes in the vault and the connections
Obsidian_(software)
Embedding a graph in a topological space, often Euclidean
graph-encoded map, an edge-colored cubic graph with four vertices for each edge of the embedded graph. The problem of finding the graph genus is NP-hard (the
Graph_embedding
Pencil and paper connection game
from the graph a non-colored edge of their choice. On Short's turn, Short colors any edge still in the graph. If Cut manages to turn the graph into one
Shannon_switching_game
Unsolved problem on graph coloring
According to the four color theorem, the resulting planar graph (or any planar graph) can be colored using at most four different colors, no matter how many
Earth–Moon_problem
Pan-genome Graph Construction Methodology
graph models for pan-genomes appeared. A notable example was the colored de Bruijn graph approach used by Cortex, which built a joint de Bruijn graph
Pan-genome_graph_construction
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
Generalization of graph theory
hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two
Hypergraph
Graph with tight clique-coloring relation
In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every
Perfect_graph
Family of symmetric graphs which generalize the Petersen graph
of graph theory, the odd graphs are a family of symmetric graphs defined from certain set systems. They include and generalize the Petersen graph. The
Odd_graph
Method for finding patterns in networks
planar graphs, it is possible to develop an algorithm that finds well-colored cycles. Here, a cycle is well-colored if its vertices are colored by consecutive
Color-coding
Clustering and community detection algorithm
that all communities are well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents
Leiden_algorithm
In mathematics, a topological graph is a representation of a graph in the plane, where the vertices of the graph are represented by distinct points and
Topological_graph
Graph with all vertices of degree 4
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
Algorithm for graph coloring
Consider the graph G = ( V , E ) {\displaystyle G=(V,E)} shown on the right. This is a wheel graph and will therefore be optimally colored by RLF. Executing
Recursive largest first algorithm
Recursive_largest_first_algorithm
Technique for visualizing complex functions
In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the
Domain_coloring
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
Study of discrete mathematical structures
continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics
Discrete_mathematics
Measure of similarity between two graphs
computer science, graph edit distance (GED) is a measure of similarity (or dissimilarity) between two graphs. The concept of graph edit distance was first
Graph_edit_distance
Special type of graph coloring
In graph theory, oriented graph coloring is a special type of graph coloring. Namely, it is an assignment of colors to vertices of an oriented graph that
Oriented_coloring
Class of mathematical games
has a neighbor colored with it), then Bob wins. If the graph is completely colored, then Alice wins. The game chromatic number of a graph G {\displaystyle
Graph_coloring_game
high-level nets (or colored Nets) introduced by K. Jensen. The main advantage of Well Formed Nets is the notion of symbolic reachability graph that is composed
Well-formed_Petri_net
Structure-preserving correspondence between node-link graphs
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a
Graph_homomorphism
Periodic spatial graph
Being an abelian covering graph of K 4 {\displaystyle K_{4}} means that the vertices of the Laves graph can be four-colored such that each vertex has
Laves_graph
Edges that hit all cycles in a graph
In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at
Feedback_arc_set
Measure of a graph's centrality, based on shortest paths
In graph theory, betweenness centrality is a measure of centrality in a graph based on shortest paths. Betweenness centrality measures how frequently a
Betweenness_centrality
Embedding a graph in 3D space with no cycles interlinked
In topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional
Linkless_embedding
Infinite graph containing all countable graphs
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with
Rado_graph
Subunit of a computational problem
from this problem to a hard problem on undirected graphs, such as the Hamiltonian cycle problem or graph coloring, would typically be based on gadgets in
Gadget_(computer_science)
Solid with 12 equal pentagonal faces
supramolecules, as well as the shape of the universe. The skeleton of a regular dodecahedron can be represented as the graph called the dodecahedral graph, a Platonic
Regular_dodecahedron
Natural number
theorem states that a planar graph (or, equivalently, a flat map of two-dimensional regions such as countries) can be colored using four colors, so that
4
Mathematical game played on a directed graph
A parity game is played on a colored directed graph, where each node has been colored by a priority – one of (usually) finitely many natural numbers. Two
Parity_game
Theorem on triangulation graph colorings
is an odd number of full-colored simplices. Here is an elaboration of the proof given previously, for a reader new to graph theory. This diagram numbers
Sperner's_lemma
Statement in mathematical combinatorics
its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. As
Ramsey's_theorem
Function in algebraic graph theory
chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function
Chromatic_polynomial
Graph which can be made planar by removing a single node
In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called
Apex_graph
Graph layout on multiple half-planes
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings in a book, a collection of half-planes all having the
Book_embedding
Theorem in extremal graph theory
it is not contained in the Turán graph T(n,r − 1), as this graph and therefore each of its subgraphs can be colored with r − 1 colors. It follows that
Erdős–Stone_theorem
Independent set which is not a subset of any other independent set
maximum independent set. The graphs in which all maximal independent sets have the same size are called well-covered graphs. The phrase "maximal independent
Maximal_independent_set
Nonconstructive method for mathematical proofs
r} vertices which is monochromatic (every edge colored the same color). To do so, we color the graph randomly. Color each edge independently with probability
Probabilistic_method
Element of graph theory
theorem states that a graph has an acyclic orientation in which the longest path has at most k vertices if and only if it can be colored with at most k colors
Acyclic_orientation
become well known and repeatedly studied and generalized in graph theory, in part because of its elegant proof using techniques from algebraic graph theory
Graham–Pollak_theorem
Base of natural logarithms
{1}{1\cdot 2\cdot 3}}+\cdots .} It is the unique positive number a such that the graph of the function y = ax has a slope of 1 at x = 0. One has e = exp ( 1
E_(mathematical_constant)
Mathematical concept in graph theory
In graph theory, an efficient dominating set (also called an e.d. set or independent perfect dominating set) is a dominating set with the additional property
Efficient_dominating_set
twin-width of an undirected graph is a natural number associated with the graph, used to study the parameterized complexity of graph algorithms. Intuitively
Twin-width
Combinatorial game theory concept to represent all possible game states
In the context of combinatorial game theory, a game tree is a graph representing all possible game states within a sequential game that has perfect information
Game_tree
Topics referred to by the same term
refer to: Cone (category theory) Cone (formal languages) Cone (graph theory), a graph in which one vertex is adjacent to all others Cone (linear algebra)
Cone_(disambiguation)
Five-pointed star polygon
space Pentalpha – Puzzle involving stones and a pentagram Petersen graph – Cubic graph with 10 vertices and 15 edges Ptolemy's theorem – Relates the 4 sides
Pentagram
Sequence of locally optimal choices
distributed hash table. Graph theory is a rich source of greedy algorithms. Computing scientists frequently use greedy algorithms to compute graph invariants. Dijkstra's
Greedy_algorithm
Type of sub-graph
recurrent and statistically significant subgraphs or patterns of a larger graph. All networks, including biological networks, social networks, technological
Network_motif
Installation art by Christian Boltanski
Boltanski first drew the piece out on paper, using pencil, colored pencil, and ink on graph paper mounted on board. That sketch, created 1987–1989, is
Monument_to_the_Lycée_Chases
Natural number
In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: K5, the complete graph with
5
crystallography, a periodic graph or crystal net is a three-dimensional periodic graph, i.e., a three-dimensional Euclidean graph whose vertices or nodes
Periodic graph (crystallography)
Periodic_graph_(crystallography)
( see it ) "holi( see it )" shows a picture of bowls of colored powder in the Knowledge Graph which, when clicked, will simulate throwing a gob of powder
List_of_Google_Easter_eggs
1038/s41586-021-03823-6. hdl:10072/407535. PMC 8387238. PMID 34433944. The qpGraph analysis confirmed this branching pattern, with the Leang Panninge individual
Genetic history of East Asians
Genetic_history_of_East_Asians
Special subset of a partially ordered set
Igarashi, Ayumi; Zwicker, William S. (16 February 2021). "Fair division of graphs and of tangled cakes". arXiv:2102.08560 [math.CO]. Davey, B. A.; Priestley
Filter_(mathematics)
Company logo
second "o" as it is distinctly more orange-colored in place of the previously more yellowish "o", as well as a much more subtle shadow rendered in a different
Google_logo
Sharpest angle between edges at a vertex
In graph drawing, the angular resolution of a drawing of a graph is the sharpest angle formed by any two edges that meet at a common vertex of the drawing
Angular resolution (graph drawing)
Angular_resolution_(graph_drawing)
Study of influence of color on human behavior
physically drawn to warm colored displays; however, they rated cool colored displays as more favorable. This implies that warm colored store displays are more
Color_psychology
Writing paper with lines
margins, act as tab stops or create a grid for plotting data; for example, graph paper (squared paper or grid paper) is divided into squares by horizontal
Ruled_paper
Complexity class
whether a graph can be colored with 2 colors is in P, but with 3 colors is NP-complete, even when restricted to planar graphs. Determining if a graph is a
NP-completeness
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
Branch of mathematics
contrast, does not solve the equation and is therefore not part of the graph. The graph encompasses the totality of ( x , y ) {\displaystyle (x,y)} -pairs
Algebra
Proving validity without revealing other data
large graph G. Victor knows G but not the cycle (e.g., Peggy has generated G and revealed it to him.) Finding a Hamiltonian cycle given a large graph is
Zero-knowledge_proof
List of Windows 10 operating system versions
("activities"). When users consent to Microsoft data collection via Microsoft Graph, activities can also be synchronized from supported Android and iOS devices
Windows_10_version_history
Conscious subjective experience
separation as valid. Nowadays, most research into emotions in the clinical and well-being context focuses on emotion dynamics in daily life, predominantly the
Emotion
American record label
Ambassador, The Third Man Recording Booth, "a refurbished 1947 Voice-o-Graph machine that can record up to two minutes audio and press it onto 6-inch
Third_Man_Records
In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph G {\displaystyle G} , find the maximal number of edges
Forbidden_subgraph_problem
Mesolithic hunter-gatherers of Iranian Plateau
from the Hotu and Kamarband Caves and Ganj Dareh, Tepe Abdul Hosein, as well as Wezmeh. A deeply diverged sister branch (at least 12,000 years BP), best
Iranian_hunter-gatherers
App by Habitics
provides several statistics displayed in charts, such as a monthly mood line graph and an average daily mood bar chart. These are automatically updated as
Daylio
Direct sum of uniform matroids
Direct sums of partition matroids are partition matroids as well. A maximum matching in a graph is a set of edges that is as large as possible subject to
Partition_matroid
Social media platform owned by Meta
2011). "At 5 Million Users, It's Hard Not To View Instagram Through A Rose-Colored Filter". TechCrunch. AOL. Retrieved April 8, 2017. Swant, Marty (December
Line of graphing calculators produced by Texas Instruments
The TI-83 series is a line of graphing calculators produced by Texas Instruments. Released in 1996, the series remained popular and widely used in schools
TI-83_series
Framework in mathematics
DTW-equivalent shortest path problem to the maximum flow problem in the dual graph, which can be solved by most max-flow algorithms. However, when the data
Graphical_time_warping
Algorithm for finding important nodes in a graph
an algorithm for calculating the betweenness centrality of vertices in a graph. The algorithm was first published in 2001 by Ulrik Brandes. Betweenness
Brandes'_algorithm
On domino tiling after removing two corners
using a Hamiltonian cycle of the grid graph formed by the chessboard squares. The removal of any two oppositely colored squares splits this cycle into two
Mutilated_chessboard_problem
Four-dimensional number system
Charles F.F. (January 2007). "Quaternions in molecular modeling". J. Mol. Graph. Mod. 25 (5): 595–604. arXiv:physics/0506177. Bibcode:2007JMGM...25..595K
Quaternion
Signal processing effect
figures below offer additional depictions of aliasing, due to sampling. A graph of amplitude vs frequency (not time) for a single sinusoid at frequency
Aliasing
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