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Graph with only one possible coloring
In graph theory, a uniquely colorable graph is a k-chromatic graph that has only one possible (proper) k-coloring up to permutation of the colors. Equivalently
Uniquely_colorable_graph
Methodic assignment of colors to elements of a graph
Critical graph Graph coloring game Graph homomorphism Hajós construction Mathematics of Sudoku Multipartite graph Uniquely colorable graph MacKenzie
Graph_coloring
Perfect graph Ramsey's theorem Sperner's lemma Strong coloring Subcoloring Tait's conjecture Total coloring Uniquely colorable graph Path (graph theory)
List_of_graph_theory_topics
Planar maps require at most four colors
that no two adjacent vertices receive the same color, or for short: every planar graph is four-colorable. As far as is known, the conjecture was first
Four_color_theorem
Assignment of colors to edges of a graph
claw K1,3, is not uniquely 3-edge-colorable. A 2012 conjecture that if G is a d-regular planar multigraph, then G is d-edge-colorable if and only if G
Edge_coloring
Graph of chess rook moves
{\displaystyle m=n=4} , these properties uniquely characterize the rook's graph. That is, the rook's graphs are the only graphs with these numbers of vertices,
Rook's_graph
Graph defined from a mathematical group
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract
Cayley_graph
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
Non-crossing graph with vertices on outer face
Every outerplanar graph is 3-colorable, and has degeneracy and treewidth at most 2. The outerplanar graphs are a subset of the planar graphs, the subgraphs
Outerplanar_graph
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
Graph that can be embedded in the plane
The four color theorem states that every planar graph is 4-colorable (i.e., 4-partite). Fáry's theorem states that every simple planar graph admits a
Planar_graph
Graph divided into two independent sets
an odd cycle. A graph is bipartite if and only if it is 2-colorable, (i.e. its chromatic number is less than or equal to 2). A graph is bipartite if and
Bipartite_graph
Conjecture in graph theory
exponential graphs: for every integer k, the graph KkG is either k-colorable, or it contains a loop (meaning G is k-colorable). One can also see the homomorphisms
Hedetniemi's_conjecture
Structure-preserving correspondence between node-link graphs
colors (i.e., it is a k-coloring). In particular, G is k-colorable if and only if it is Kk-colorable. If there are two homomorphisms G → H and H → Kk, then
Graph_homomorphism
Graph with all vertices of degree 4
J. (1973), "Regular n-valent n-connected nonHamiltonian non-n-edge-colorable graphs", Journal of Combinatorial Theory, Series B, 14: 55–60, doi:10
Quartic_graph
Family of cubic graphs formed from regular and star polygons
Thomason, Andrew (1982), "Cubic graphs with three Hamiltonian cycles are not always uniquely edge colorable", Journal of Graph Theory, 6 (2): 219–221, doi:10
Generalized_Petersen_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
Graph representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
Cubic graph with 28 vertices and 42 edges
Coxeter graph, referenced as F28A, is the only cubic symmetric graph on 28 vertices. The Coxeter graph is also uniquely determined by its graph spectrum
Coxeter_graph
Graph coloring related to treedepth
the uniquely colored vertices of each component. For q > n {\displaystyle q>n} , where n {\displaystyle n} is the number of vertices in the graph, it
Centered_coloring
Assignment of colors to graph vertices that destroys all symmetries
for a cycle graph. With such a coloring, each key will be uniquely identified by its color and the sequence of colors surrounding it. A graph has distinguishing
Distinguishing_coloring
Intuitively, the target (base) graph is "covered" by the source (total) graph in such a way that each arc of the base can be uniquely lifted to any node in the
Fibrations_of_graphs
Cycle graph plus universal vertex
In graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can
Wheel_graph
Graph formed by subdivision of triangles
every uniquely 4-colorable planar graph is an Apollonian network. Therefore, Apollonian networks may also be characterized as the uniquely 4-colorable planar
Apollonian_network
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
Graph formed by complementation and disjoint union
In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation
Cograph
Unrelated vertices in graphs
even Max Independent Set on 3-regular 3-edge-colorable graphs is APX-complete. An interval graph is a graph in which the nodes are 1-dimensional intervals
Independent set (graph theory)
Independent_set_(graph_theory)
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
Geometry with 7 points and 7 lines
particular graph is a connected cubic graph (regular of degree 3), has girth 6 and each part contains 7 vertices. It is the Heawood graph, the unique 6-cage
Fano_plane
Length of a shortest cycle contained in the graph
Petersen graph is the unique 5-cage (it is the smallest cubic graph of girth 5), the Heawood graph is the unique 6-cage, the McGee graph is the unique 7-cage
Girth_(graph_theory)
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
testing whether two graphs are isomorphic. While it solves graph isomorphism on almost all graphs, there are graphs such as all regular graphs that cannot be
Colour_refinement_algorithm
Unsolved problem in computational complexity theory
below). Linial observed that unique label cover is an instance of the Maximum Section of a Covering Graph problem (covering graphs is the terminology from
Unique_games_conjecture
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the
Signal-flow_graph
Every graph has evenly many odd vertices
In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges
Handshaking_lemma
Abstract mathematical system of two types of objects and a relation between them
called the Levi graph or incidence graph of the structure. As any bipartite graph is two-colorable, the Levi graph can be given a black and white vertex
Incidence_structure
Study of influence of color on human behavior
referential theory of color, color may convey two types of meaning that uniquely stimulate and shape consumer preferences and behaviors. Referential meaning
Color_psychology
Generalization of graph coloring to the hypergraph
assignment of a color to each vertex of V. A coloring is conflict-free if at least one vertex in each edge has a unique color. If H is a graph, then this condition
Conflict-free_coloring
Graph used in computational complexity theory and graph theory
Frankl–Rödl graphs with this parameter value have high chromatic number, semidefinite programming is unable to distinguish them from 3-colorable graphs. However
Frankl–Rödl_graph
Algorithm in graph theory
{\displaystyle \Delta } is the maximum degree of the graph. This is optimal for some graphs, and it uses at most one color more than optimal for all others. The existence
Misra & Gries edge-coloring algorithm
Misra_&_Gries_edge-coloring_algorithm
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
Number denoting a graph's closeness to a tree
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest
Treewidth
Balanced complete multipartite graph
graph into independent sets corresponds to the partition of G into color classes. In particular, the Turán graph is the unique maximal n-vertex graph
Turán_graph
Planar graph with 23 vertices and 63 edges
In the mathematical field of graph theory, the Kittell graph is a planar graph with 23 vertices and 63 edges. Its unique planar embedding has 42 triangular
Kittell_graph
Mathematical tree with cycle through leaves
In graph theory, a Halin graph is a type of planar graph, constructed by connecting the leaves of a tree into a cycle. The tree must have at least four
Halin_graph
Edge-face adjacencies in another graph
graph theory, the medial graph of plane graph G is another graph M(G) that represents the adjacencies between edges in the faces of G. Medial graphs were
Medial_graph
Clustering and community detection algorithm
well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents a community). Additionally, the center
Leiden_algorithm
Graph with a median for each three vertices
In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a {\displaystyle a} , b {\displaystyle
Median_graph
Computer compiler optimization technique
register allocation), or across function boundaries traversed via call-graph (interprocedural register allocation). When done per function/procedure
Register_allocation
Algorithmic application of graph theory
extraction is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled based on a given heuristic. Connected-component
Connected-component_labeling
Algorithm in computer graphics to add color or texture
explicit graph theory to the problem, treating spans of pixels, or aggregates of such, as nodes and studying their connectivity. The first published graph theory
Flood_fill
Graph coloring avoiding 2-colored paths
In the mathematical field of graph theory, a star coloring of a graph G is a (proper) vertex coloring in which every path on four vertices uses at least
Star_coloring
Type of mathematical expression
polynomial is also unique in that it is the only polynomial in one indeterminate that has an infinite number of roots. The graph of the zero polynomial
Polynomial
Periodic spatial graph
Laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional Euclidean space, forming a periodic graph. Three
Laves_graph
Convex polyhedron with 14 triangle faces
Alfred Kempe's attempted proof of the four color theorem was incorrect. The Fritsch graph is one of only six graphs in which every neighborhood is a 4- or
Triaugmented_triangular_prism
Pictorial representation of the behavior of subatomic particles
eventually erases all the Fermionic lines: this is the Euler algorithm to 2-color a graph, which works whenever each vertex has even degree. The number of steps
Feynman_diagram
Sequence of locally optimal choices
minimum spanning trees of a given connected graph. They always find an optimal solution, which may not be unique in general. A greedy algorithm constructs
Greedy_algorithm
Ability to perceive differences in light frequency
the Visual Experience of Very Bright and Very Dark Scenes". ACM Trans. Graph. 34 (3): 15. doi:10.1145/2714573. S2CID 14960893. Biggs T, McPhail S, Nassau
Color_vision
Block puzzle with four colored cubes
cube is unique, and the order in which the four cubes are stacked is irrelevant as long as each side shows every color. This problem has a graph-theoretic
Instant_Insanity
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
Special type of graph coloring
colors, then it corresponds uniquely to a graph homomorphism into a tournament. The tournament has one vertex for each color in the coloring. For each pair
Oriented_coloring
Ability of a light source to reproduce colors
chroma, a gamut shape graph, and detailed values for chroma, hue, and color fidelity for each of the 16 hue ranges, plus color fidelity scores for each
Color_rendering
{\displaystyle k\in \mathbb {N} } , a k {\displaystyle k} -graph (also known as a higher-rank graph or graph of rank k {\displaystyle k} ) is a countable category
K-graph_C*-algebra
Theorem in extremal graph theory
the number of edges of the Turán graph T(n, r − 1), and that the Turán graph is the unique such extremal graph. The Erdős–Stone theorem extends this
Erdős–Stone_theorem
Directed graph isomorphic to its own transpose graph
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by
Skew-symmetric_graph
Four-dimensional analogue of the cube
Mathematical Society: 18. MR 0304504. Pournin, Lionel (2013). "The flip-Graph of the 4-dimensional cube is connected". Discrete & Computational Geometry
Tesseract
Property of objects inherited by all their subobjects
graph classes are independent graphs (graphs with no edges), which is a special case (with c = 1) of being c-colorable for some number c, being forests
Hereditary_property
Edge-colored graph matching where all edges have distinct colors
edge-colored bipartite graphs. Rainbow matchings have been applied for solving packing problems. Rainbow coloring Rainbow-colorable hypergraph Rainbow-independent
Rainbow_matching
Archimedean solid with 26 faces
In the mathematical field of graph theory, a truncated cuboctahedral graph (or great rhombcuboctahedral graph) is the graph of vertices and edges of the
Truncated_cuboctahedron
Programming paradigm focused on difficult search problems
of a graph G = ⟨ V , E ⟩ {\displaystyle G=\left\langle V,E\right\rangle } is a function c o l o r : V → { 1 , … , n } {\displaystyle \mathrm {color} :V\to
Answer_set_programming
Polygenic phenotypic characteristic
(2003). "An Ocularist's Approach to Human Iris Synthesis". IEEE Comput. Graph. Appl. 23 (6): 70–5. doi:10.1109/MCG.2003.1242384. S2CID 537404. "Where
Eye_color
Visual representation of data
imagery. The visual formats used in data visualization includes charts and graphs, geospatial maps, figures, correlation matrices, percentage gauges, etc
Data and information visualization
Data_and_information_visualization
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
Free online crowdsourced encyclopedia
be due to errors in counting, other experts feel that Google's Knowledge Graphs project launched last year may be gobbling up Wikipedia users." When contacted
Wikipedia
Visual artifact that depicts or records perception
image does not need to be real; it may be an abstract concept such as a graph or function or an imaginary entity. For a mental image to be understood
Image
Graph in climate science
Hockey stick graphs present global or hemispherical mean global surface temperatures of the distant past, as shown by quantitative climate reconstructions
Hockey stick graph (global temperature)
Hockey_stick_graph_(global_temperature)
Convex polytope, the n-dimensional analogue of a square and a cube
an example of a zonotope. The 1-skeleton of a hypercube is a hypercube graph. A unit hypercube of dimension n {\displaystyle n} is the convex hull of
Hypercube
Combinatorial representation of a graph on an orientable surface
a graph on an orientable surface. A combinatorial map may also be called a combinatorial embedding, a rotation system, an orientable ribbon graph, a
Combinatorial_map
Semiconductor light source
mode. Uniquely, this type of LED would conduct when connected backwards. Color: LEDs can emit light of an intended color without using any color filters
Light-emitting_diode
Pseudolines arranged largely to study arrangements of lines
stretchability). These graphs have several other notable combinatorial properties: They are 4-edge-colorable and 3-vertex-colorable The diameter on n {\displaystyle
Arrangement_of_pseudolines
attained uniquely by the Turán graph T n , r {\displaystyle T_{n,r}} . Both of these classic results ask questions about how large a graph can be before
Ramsey-Turán_theory
Mathematical function, denoted exp(x) or e^x
v+iw=\exp(x+iy)} the graph of the exponential function is a two-dimensional surface curving through four dimensions. Starting with a color-coded portion of
Exponential_function
Polyhedron with four faces
{\displaystyle K_{4}} because every pair of its vertices has a unique edge. In a plane, this graph can be regarded as a triangle in which three vertices connect
Tetrahedron
Class of algorithms
tree uniquely. Given a tree with distinct elements, either pre-order or post-order paired with in-order is sufficient to describe the tree uniquely. However
Tree_traversal
Independent set in a graph
In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E)
Rainbow-independent_set
Knowledge Graph which when clicked, makes confetti explode. "panipuri( see it )" will show three types of panipuris in the Knowledge Graph, which when
List_of_Google_Easter_eggs
with property B is also called 2-colorable. Sometimes it is also called bipartite, by analogy to the bipartite graphs (see bipartite hypergraph). Property
Property_B
Software resource tracking technique
collection schemes, it is often helpful to think of the reference graph, which is a directed graph where the vertices are objects and there is an edge from an
Reference_counting
Algorithm for division of polynomials
= 0 or the degree of R is lower than the degree of B. These conditions uniquely define Q and R; the result R = 0 occurs if and only if the polynomial A
Polynomial_long_division
Clustering and community detection algorithm
each node v in a graph to be its own community. This can be seen in Figure 1, where each dot (representing nodes) is a unique color (representing which
Louvain_method
Data modeling construct
action is taken. Named graphs and quads, an extension to semantic triples to also include a context node as a fourth element. Graph database Link relation
Semantic_triple
Graphic visual representation of information
are commonly used to show the weather, as well as maps, site plans, and graphs for summaries of data. Some books are almost entirely made up of information
Infographic
Plane curve: conic section
parallel to another plane that is tangential to the conical surface. The graph of a quadratic function y = a x 2 + b x + c {\displaystyle y=ax^{2}+bx+c}
Parabola
Formal language for describing data models
Resource Description Framework (RDF) is a method to describe and exchange graph data. It was originally designed as a data model for metadata by the World
Resource Description Framework
Resource_Description_Framework
of graph, a clique graph, where each k-clique in the original graph is represented by a vertex in the new clique graph. The edges in the clique graph are
Clique_percolation_method
Generalizations in graph theory
hypergraph). Here we define a hypergraph as bipartite if it is exactly 2-colorable, i.e., its vertices can be 2-colored such that each hyperedge contains
Hall-type theorems for hypergraphs
Hall-type_theorems_for_hypergraphs
Virtual keyboard app for Android and iOS
additional functionality, including GIF suggestions, options for a dark color theme or adding a personal image as the keyboard background, support for
Gboard
decrease percentage. A graph shows the trends of each company over time, with a green graph showing positive growth and a red graph showing a decline. Business
List_of_built-in_macOS_apps
Divination method
Arabic loan-word into French tassa, and the respective Greek suffixes -graph (writing), -mancy (divination), and -logy (study of). Tasseomancy followed
Tasseography
Fractal named after mathematician Benoit Mandelbrot
axes() ax.set_aspect("equal") graph = ax.pcolormesh(x_domain, y_domain, iteration_array, cmap=colormap) plt.colorbar(graph) plt.xlabel("Real-Axis") plt
Mandelbrot_set
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UNIQUELY COLORABLE-GRAPH
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