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Number of planar subgraphs to cover a graph
In graph theory, the thickness of a graph G is the minimum number of planar graphs into which the edges of G can be partitioned. That is, if there exists
Thickness_(graph_theory)
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)
4-regular undirected graph in mathematics
In the mathematical field of graph theory, the Robertson graph or (4,5)-cage, is a 4-regular undirected graph with 19 vertices and 38 edges named after
Robertson_graph
Topics referred to by the same term
Look up thickness in Wiktionary, the free dictionary. Thickness may refer to: Thickness (graph theory) Thickness (geology), the distance across a layer
Thickness
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 layout on multiple half-planes
the exact book thickness for complete graphs. The graphs with book thickness one are the outerplanar graphs. The graphs with book thickness at most two are
Book_embedding
Graph that can be embedded in the plane
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect
Planar_graph
discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey theory, dynamical systems, and partial
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Graph of numbers differing by a square
the number theory of quadratic residues, and have interesting properties that make them useful in graph theory more generally. Paley graphs are named after
Paley_graph
Hypohamiltonian graph in graph theory
graph is, in graph theory, a hypohamiltonian graph with 16 vertices and 27 edges. It has book thickness 3 and queue number 2. Hypohamiltonian graphs were
Sousselier_graph
Embedding a graph in a topological space, often Euclidean
In topological graph theory, an embedding (also spelled imbedding) of a graph G {\displaystyle G} on a surface Σ {\displaystyle \Sigma } is a representation
Graph_embedding
One of two different regular graphs with 16 vertices
field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with
Clebsch_graph
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)
In the mathematical field of graph theory, the Brinkmann graph is a 4-regular graph with 21 vertices and 42 edges discovered by Gunnar Brinkmann in 1992
Brinkmann_graph
Undirected graph with 14 vertices
mathematical field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood. The graph is cubic, and
Heawood_graph
Method of graph decomposition
In graph theory, a bramble for an undirected graph G is a family of connected subgraphs of G that all touch each other: for every pair of disjoint subgraphs
Bramble_(graph_theory)
Undirected graph named after S. S. Shrikhande
mathematical field of graph theory, the Shrikhande graph is a graph discovered by S. S. Shrikhande in 1959. It is a strongly regular graph with 16 vertices
Shrikhande_graph
Graph with at most one crossing per edge
In topological graph theory, a 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing
1-planar_graph
Directed graph representing overlaps between sequences of symbols
In graph theory, an n-dimensional De Bruijn graph of m symbols is a directed graph representing overlaps between sequences of symbols. It has mn vertices
De_Bruijn_graph
Bipartite, 3-regular undirected graph
field of graph theory, the Pappus graph is a bipartite, 3-regular, undirected graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus
Pappus_graph
In graph theory, the Holt graph or Doyle graph is the smallest half-transitive graph, that is, the smallest example of a vertex-transitive and edge-transitive
Holt_graph
Cubic graph with 28 vertices and 42 edges
field of graph theory, the Coxeter graph is a 3-regular graph with 28 vertices and 42 edges. It is one of the 13 known cubic distance-regular graphs. It is
Coxeter_graph
mathematical field of graph theory, the Ellingham–Horton graphs are two 3-regular graphs on 54 and 78 vertices: the Ellingham–Horton 54-graph and the Ellingham–Horton
Ellingham–Horton_graph
Undirected graph with 11 nodes and 27 edges
In the mathematical field of graph theory, the Goldner–Harary graph is a simple undirected graph with 11 vertices and 27 edges. It is named after Anita
Goldner–Harary_graph
Two special graphs in graph theory
In the mathematical field of graph theory, the Klein graphs are two different but related regular graphs, each with 84 edges. Each can be embedded in
Klein_graphs
Regular graph with 70 nodes and 105 edges
field of graph theory, the Harries graph or Harries (3-10)-cage is a 3-regular, undirected graph with 70 vertices and 105 edges. The Harries graph has chromatic
Harries_graph
Triangle-free graph requiring four colors
In the mathematical field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number
Grötzsch_graph
Bipartite 4-regular graph with 20 nodes and 40 edges
mathematical field of graph theory, the Folkman graph is a 4-regular graph with 20 vertices and 40 edges. It is a regular bipartite graph with symmetries taking
Folkman_graph
Invariant in graph theory
mathematical field of graph theory, the queue number of a graph is a graph invariant defined analogously to stack number (book thickness) using first-in first-out
Queue_number
Graph with 24 vertices and 36 edges
mathematical field of graph theory, the McGee graph or the (3-7)-cage is a 3-regular graph with 24 vertices and 36 edges. The McGee graph is the unique (3
McGee_graph
graph theory, the Chvátal graph is an undirected graph with 12 vertices and 24 edges, discovered by Václav Chvátal in 1970. It is the smallest graph that
Chvátal_graph
Bipartite 3-regular graph with 90 vertices and 135 edges
mathematical field of graph theory, the Foster graph is a bipartite 3-regular graph with 90 vertices and 135 edges. The Foster graph is Hamiltonian and has
Foster_graph
Infinite family of graphs
In the mathematical field of graph theory, the flower snarks form an infinite family of snarks introduced by Rufus Isaacs in 1975. As snarks, the flower
Flower_snark
2018 mathematics book by Marcus Schaefer
third chapter relating the crossing number to graph parameters including skewness, bisection width, thickness, and (via the Albertson conjecture) the chromatic
Crossing_Numbers_of_Graphs
In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck. It is Hamiltonian
Dyck_graph
Theorem about infinite graphs
In graph theory, a branch of mathematics, Halin's grid theorem states that the infinite graphs with thick ends are exactly the graphs containing subdivisions
Halin's_grid_theorem
Distance-transitive cubic graph with 20 nodes and 30 edges
In the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after
Desargues_graph
In the mathematical field of graph theory, the Hoffman graph is a 4-regular graph with 16 vertices and 32 edges discovered by Alan Hoffman. Published in
Hoffman_graph
4-regular undirected graph with 70 vertices and 140 edges
In the mathematical field of graph theory, the Meredith graph is a 4-regular undirected graph with 70 vertices and 140 edges discovered by Guy H. J. Meredith
Meredith_graph
3-regular graph with 30 vertices and 45 edges
mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage or Cremona–Richmond graph is a 3-regular graph with 30 vertices and 45
Tutte–Coxeter_graph
Graph containing cycles of all possible lengths
In the mathematical study of graph theory, a pancyclic graph is a directed graph or undirected graph that contains cycles of all possible lengths from
Pancyclic_graph
Unsolved problem on graph coloring
Thom (2008), "Thickness-two graphs, I: New nine-critical graphs, permuted layer graphs, and Catlin's graphs", Journal of Graph Theory, 57 (3): 198–214
Earth–Moon_problem
American mathematician
1940 – 25 October 2020) was an American mathematician specializing in graph theory. He spent his teaching career at Texas A&M University. Arthur Hobbs was
Arthur_Hobbs_(mathematician)
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
Cubic graph with 70 nodes and 105 edges
In the mathematical field of graph theory, the Balaban 10-cage or Balaban (3,10)-cage is a 3-regular graph with 70 vertices and 105 edges named after
Balaban_10-cage
and an upper bound on its book thickness is 5. Brouwer, A. E.; Cohen, A. M.; Neumaier, A. (1989), Distance-Regular Graphs, Springer-Verlag, Theorem 9.2
Wells_graph
Operation combining two oriented knots
of mathematics that studies knots is known as knot theory and has many relations to graph theory. A knot is an embedding of the circle (S1) into three-dimensional
Knot_(mathematics)
mathematical field of graph theory, the Harries–Wong graph is a 3-regular undirected graph with 70 vertices and 105 edges. The Harries–Wong graph has chromatic
Harries–Wong_graph
In the mathematical field of graph theory, the double-star snark is a snark with 30 vertices and 45 edges. In 1975, Rufus Isaacs introduced two infinite
Double-star_snark
Snark with 50 vertices and 75 edges
graph theory, the Watkins snark is a snark with 50 vertices and 75 edges. It was discovered by John J. Watkins in 1989. As a snark, the Watkins graph
Watkins_snark
24-vertex symmetric bipartite cubic graph
In the mathematical field of graph theory, the Nauru graph is a symmetric, bipartite, cubic graph with 24 vertices and 36 edges. It was named by David
Nauru_graph
Subgraph of planar graph with Hamiltonian cycle
In graph theory and graph drawing, a subhamiltonian graph is a subgraph of a planar Hamiltonian graph. A graph G is subhamiltonian if G is a subgraph
Subhamiltonian_graph
In the mathematical field of graph theory, the Horton graph or Horton 96-graph is a 3-regular graph with 96 vertices and 144 edges discovered by Joseph
Horton_graph
American mathematician
theory, AT White, LW Beineke, Selected Topics in Graph Theory, 1978 "The thickness of the complete graph", LW Beineke, Frank Harary – Canadian Journal of Mathematics
L._W._Beineke
Szekeres snark with 50 tops and 75 edges
In the mathematical field of graph theory, the Szekeres snark is a snark with 50 vertices and 75 edges. It was the fifth known snark, discovered by George
Szekeres_snark
mathematical field of graph theory, the Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches
Gray_graph
Modelling the appearance of paint coatings
thickness. Kubelka derived many additional formulas for a variety of other cases, which were published in the post-war years. Whereas the 1931 theory
Kubelka–Munk_theory
Archimedean solid with 14 faces
edges, and is a cubic Archimedean graph. It has book thickness 3 and queue number 2. As a Hamiltonian cubic graph, it can be represented by LCF notation
Truncated_octahedron
Number of forests a graph's edges may be partitioned into
Westermann 1992). The subgraph density of a graph is the density of its densest subgraph. The thickness of a graph is the minimum number of planar subgraphs
Arboricity
Symmetric bipartite cubic graph with 16 vertices and 24 edges
In the mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August
Möbius–Kantor_graph
Graphical representations of connectomics
connections in the human brain. These circular graphs based on diffusion MRI data utilize graph theory to demonstrate the white matter connections and
Connectogram
edges of a given graph, and geometric thickness, the minimum number of edge colors needed in a straight-line drawing of a given graph with no crossing
Simultaneous_embedding
Graphical representation of energy flows in physical systems
A bond graph is a graphical representation of the energy flows though and between physical dynamical systems including those in the electrical, mechanical
Bond_graph
Number of edge slopes in graph drawing
In graph drawing and geometric graph theory, the slope number of a graph is the minimum possible number of distinct slopes of edges in a drawing of the
Slope_number
Film lubrication versus surface friction
lubrication sub-problem can be represented via a central film thickness fit to calculate the film thickness and the Greenwood-Williamson model for the “dry” contact
Stribeck_curve
Family of graphs whose shallow minors are sparse graphs
In graph theory, a family of graphs is said to have bounded expansion if all of its shallow minors are sparse graphs. Many natural families of sparse
Bounded_expansion
Problem in network theory
for other kinds of embeddings Book thickness Graph thickness Doubly connected edge list Regular map (graph theory) Fáry's theorem Node2vec Statistical
Link_prediction
tree problem. Feedback vertex set Feedback arc set Graph coloring Graph homomorphism problem Graph partition into subgraphs of specific types (triangles
List_of_NP-complete_problems
In graph theory, a branch of mathematics, the linear arboricity of an undirected graph is the smallest number of linear forests its edges can be partitioned
Linear_arboricity
Two 3-regular graphs with 18 vertices and 27 edges
In the mathematical field of graph theory, the Blanuša snarks are two 3-regular graphs with 18 vertices and 27 edges. They were discovered by Yugoslavian
Blanuša_snarks
Dielectric mirror that selectively reflects a particular wavelength range of light
refractive index profiles of a Rugate and a Bragg mirror are shown in the graph on the right. In Bragg mirrors, the discontinuous transitions are responsible
Rugate_filter
Study of the practices and possibilities of music
Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. The Oxford Companion to Music describes
Music_theory
Graph drawing with vertices on a line
Bernhart, Frank R.; Kainen, Paul C. (1979), "The book thickness of a graph", Journal of Combinatorial Theory, Series B, 27 (3): 320–331, doi:10.1016/0095-8956(79)90021-2
Arc_diagram
Hypothetical vacuum, less stable than true vacuum
In quantum field theory, a false vacuum is a hypothetical vacuum state that is locally stable but does not occupy the most stable possible ground state
False_vacuum
Uranium processed to increase the percentage of uranium-235
p. 27. Retrieved 1 July 2019. Olander, Donald R. (1 January 1981). "The theory of uranium enrichment by the gas centrifuge". Progress in Nuclear Energy
Enriched_uranium
Fan that induces gas flow mostly parallel to the shaft
are two dominant theories that solve the parameters for axial fans: Slipstream Theory Blade Element Theory In the figure, the thickness of the propeller
Axial_fan_design
Curve along which a 3-D surface is at equal elevation
equal value to the state. It is a plane section of the three-dimensional graph of the function f ( x , y ) {\displaystyle f(x,y)} parallel to the ( x
Contour_line
Biological causes of variation in human personality
biologically based personality theories such as Eysenck's three factor model of personality, Grey's reinforcement sensitivity theory (RST), and Cloninger's model
Biological basis of personality
Biological_basis_of_personality
Total mass of fat divided by total body mass
developed different recommendations for ideal body fat percentages. This graph from the National Health and Nutrition Examination Survey (NHANES) in the
Body_fat_percentage
American mathematician
Bernhart, Frank R.; Kainen, Paul C. (1979), "The book thickness of a graph", Journal of Combinatorial Theory, Series B, 27 (3): 320–331, doi:10.1016/0095-8956(79)90021-2
Paul_Chester_Kainen
as its length, width, thickness, boundary constraints, and abrupt changes in geometry, such as holes, are considered. The theory began with the consideration
Strength_of_materials
The theory of solar cells explains the process by which light energy in photons is converted into electric current when the photons strike a suitable semiconductor
Theory_of_solar_cells
Threshold of percolation theory models
models on lattices Graph theory Network science Percolation Percolation critical exponents Percolation theory Continuum percolation theory Random sequential
Percolation_threshold
Method of approximating the properties of a composite material
materials science, effective medium approximations (EMA) or effective medium theory (EMT) pertain to analytical or theoretical modeling that describes the macroscopic
Effective medium approximations
Effective_medium_approximations
Elastic waves propagating in solid plates or spheres
across the thickness of the plate. Although the lamb wave pioneers worked on non-destructive testing applications and drew attention to the theory, widespread
Lamb_waves
unit kelvin the functors of K-theory an unspecified (real) constant a field in algebra with a subscript, a complete graph on that many vertices the area
Latin letters used in mathematics, science, and engineering
Latin_letters_used_in_mathematics,_science,_and_engineering
Layer of gases surrounding an astronomical body held by gravity
volatiles, creating the secondary atmosphere. The original composition and thickness of the atmosphere is thus determined by the stellar nebula's chemistry
Atmosphere
Opening paragraph of an article, chapter, or other written work
(summary) Editorial Introduction (writing) Inverted pyramid (journalism) Nut graph Opening sentence Carol (November 28, 2000). "The Mavens' Word of the Day:
Lead_paragraph
Knot invariant
C {\displaystyle C} and τ ( C ) {\displaystyle \tau (C)} is the knot thickness of C {\displaystyle C} . Ropelength can be turned into a knot invariant
Ropelength
Spectral density of light emitted by a black body
radiation can be compared to black-body radiation at about 5778 K (but see graph). The table on the right shows how the radiation of a black body at this
Planck's_law
Fluid dynamics theory on gravity waves
In fluid dynamics, Airy wave theory (often referred to as linear wave theory) gives a linearised description of the propagation of gravity waves on the
Airy_wave_theory
Condition when the angle of deviation is minimal in a prism
angle of emergence equal each other (i = e). This is clearly visible in the graph below. The formula for minimum deviation can be derived by exploiting the
Minimum_deviation
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
Theory in Earth sciences
sedimentary succession in excess of 6 km in thickness. The graph shows that the relations between thicknesses of all corresponding layers in these two cross-sections
Perspective geological correlation
Perspective_geological_correlation
Description of limiting behavior of a function
of probability distributions (Edgeworth series). The Feynman graphs in quantum field theory are another example of asymptotic expansions which often do
Asymptotic_analysis
Focus of social network research
represent disproportionately large social structures (based on cortical thickness in the brain). Research suggests that this is, at least in part, due to
Cognitive_social_structures
hub and t refers to the tip. The values of Fθ and δ* are derived from the graph or chart. The main points to consider are: The rotation of a rotor in turbomachinery
Three-dimensional losses and correlation in turbomachinery
Three-dimensional_losses_and_correlation_in_turbomachinery
History of research by Augustin-Jean Fresnel
which reinforce or cancel each other according to the wavelength and the thickness. Young similarly explained the colors of "striated surfaces" (e.g., gratings)
Fresnel's_physical_optics
Church in Ternopil Oblast, Ukraine
vault not through the solid thickness of the walls, but thanks to a system of buttresses built directly into the thickness of the walls of the nave. This
Church of the Translation of the Relics of Saint Nicholas, Zbruchanske
Church_of_the_Translation_of_the_Relics_of_Saint_Nicholas,_Zbruchanske
Mathematical theory
considered (giving the convex hull a certain thickness). This is then combined with methods from the theory of mixed volumes and geometry of numbers by
Finite_sphere_packing
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