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Intersection graph for a set of arcs on a circle
In graph theory, a circular-arc graph is the intersection graph of a set of arcs on the circle. It has one vertex for each arc in the set, and an edge
Circular-arc_graph
Part of a circle between two points
A circular arc is the arc of a circle between a pair of distinct points. If the two points are not directly opposite each other, one of these arcs, the
Circular_arc
Graph representing intersections between given sets
intervals on the real line A circular arc graph is defined as the intersection graph of arcs on a circle. A polygon-circle graph is defined as the intersection
Intersection_graph
graph (a coloring) that assigns different colors to the endpoints of each edge; see color. 3. A proper interval graph or proper circular arc graph is
Glossary_of_graph_theory
Directed graph with no directed cycles
called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is
Directed_acyclic_graph
Intersection graph of a chord diagram
algorithms, Gioan et al. (2013) presented an algorithm for recognizing circular graphs in near-linear time. Their method is slower than linear by a factor
Circle_graph
Graph with nodes connected in a closed chain
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if
Cycle_graph
Intersection graph for intervals on the real number line
of the interval graphs is G {\displaystyle G} . The intersection graphs of arcs of a circle form circular-arc graphs, a class of graphs that contains the
Interval_graph
Graph without four-vertex star subgraphs
The same is true more generally for proper circular-arc graphs. The Moser spindle, a seven-vertex graph used to provide a lower bound for the chromatic
Claw-free_graph
Graph drawing with vertices on a line
An arc diagram is a style of graph drawing, in which the vertices of a graph are placed along a line in the Euclidean plane and edges are drawn using
Arc_diagram
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
Graph drawing with vertices on a circle
In graph drawing, a circular layout is a style of drawing that places the vertices of a graph on a circle, often evenly spaced so that they form the vertices
Circular_layout
Topics referred to by the same term
Arc in Wiktionary, the free dictionary. Arc may refer to: Arc (geometry), a segment of a differentiable curve Circular arc, a segment of a circle Arc
Arc
Problem of finding the longest simple path for a given graph
classes of circular-arc graphs and of co-comparability graphs (i.e. of the complements of comparability graphs, which also contain permutation graphs), both
Longest_path_problem
Vertices connected in pairs by edges
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some
Graph_(discrete_mathematics)
Distance along a curve
{\displaystyle \pi .} If the arc is a semicircle, then s = π r . {\displaystyle s=\pi r.} For an arbitrary circular arc: If θ {\displaystyle \theta }
Arc_length
Fewest cliques covering a graph's edges
to find the intersection number in linear time in circular-arc graphs. However, although these graphs have only a polynomial number of cliques to choose
Intersection number (graph theory)
Intersection_number_(graph_theory)
Graph with tight clique-coloring relation
triangulated graphs, comparability graphs, proper interval graphs, proper circular-arc graphs, and nested interval graphs". Journal of Graph Theory. 6 (3):
Perfect_graph
Visualization of node-link graphs
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional
Graph_drawing
Sharpest angle between edges at a vertex
drawings of graphs, later authors have also investigated the angular resolution of drawings in which the edges are polygonal chains, circular arcs, or spline
Angular resolution (graph drawing)
Angular_resolution_(graph_drawing)
Physical simulation to visualize graphs
Force-directed graph drawing algorithms are a class of algorithms for drawing graphs in an aesthetically-pleasing way. Their purpose is to position the
Force-directed_graph_drawing
Canadian mathematician and computer scientist
"List homomorphisms and circular arc graphs" with Tomas Feder and Jing Huang. He is a managing editor of the Journal of Graph Theory, and was named a
Pavol_Hell
Inverse functions of sin, cos, tan, etc.
correspond to an arc whose length is rθ, where r is the radius of the circle. Thus in the unit circle, the cosine of x function is both the arc and the angle
Inverse trigonometric functions
Inverse_trigonometric_functions
Intersection graph of trapezoids between parallel lines
They are a superclass of the trapezoid graph class, and also contain circle graphs and circular-arc graphs. A circle trapezoid is the region in a circle
Trapezoid_graph
Geometric line segment whose endpoints lie on a circular arc
of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a
Chord_(geometry)
Mathematical functions
way circular angle measure is the arc length of an arc of the unit circle in the Euclidean plane or twice the area of the corresponding circular sector
Inverse_hyperbolic_functions
Intersection graph of convex polygons whose vertices lie on a common circle
intersection graphs of trapezoids that all have their vertices on the same two parallel lines. They also include the circular arc graphs. Polygon-circle graphs are
Polygon-circle_graph
Representation of a graph as a path graph "thickened" by some amount
the complements of chordal graphs, for permutation graphs, for cographs, for circular-arc graphs, for the comparability graphs of interval orders, and of
Pathwidth
Independent set which is not a subset of any other independent set
algorithms for generating all maximal independent sets of interval, circular-arc and chordal graphs", Journal of Algorithms, 5: 22–35, doi:10.1016/0196-6774(84)90037-3
Maximal_independent_set
Graph layout on multiple half-planes
also has applications in graph drawing, where two of the standard visualization styles for graphs, arc diagrams and circular layouts, can be constructed
Book_embedding
Archimedean solid with 62 faces
not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane. This polyhedron is topologically related as a part of
Rhombicosidodecahedron
Graph representing tangency between geometric objects
penny graphs. Representations as contact graphs of triangles, rectangles, squares, line segments, or circular arcs have also been studied. Chaplick, Steven;
Contact_graph
Conjecture in graph theory
In graph theory, Hedetniemi's conjecture, formulated by Stephen T. Hedetniemi in 1966, concerns the connection between graph coloring and the tensor product
Hedetniemi's_conjecture
On tangency patterns of circles
any subcubic planar graph, a drawing resembling a two-dimensional soap bubble foam in which the edges are drawn as circular arcs that meet at equal angles
Circle_packing_theorem
Circular statistical graph of proportionality
circle chart) is a circular statistical graphic which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice
Pie_chart
Theorem relating graph minors and topological embeddings
Klein bottle and so on. A graph embeds on a surface if the graph can be drawn on the surface as a set of points (vertices) and arcs (edges) that do not cross
Graph_structure_theorem
Indian-born American mathematician (1932–2024)
Laskar has often contributed to the theory of domination number and circular arc graphs. She wrote four papers with Paul Erdős, giving her an Erdős number
Renu_C._Laskar
Numerical invariant of graphs
time on interval graphs, as well as on permutation, trapezoid, circular-arc, circular permutation graphs, and cocomparability graphs of bounded dimension
Tree-depth
Archimedean solid with 62 faces
not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane. Schlegel diagrams are similar, with a perspective projection
Truncated_icosidodecahedron
Convex plane region bounded by two circular arcs
convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both arcs must bow outwards (convex-convex)
Lens_(geometry)
Graph representing leaves of a given tree graph
030. Raychaudhuri, A. (1992), "On powers of strongly chordal graphs and circular arc graphs", Ars Combinatoria, 34: 147–160. Eppstein, D.; Havvaei, H. (2020)
Leaf_power
Mathematical idealization of the trace left by a moving point
is an arc of a circle, called a circular arc. In a sphere (or a spheroid), an arc of a great circle (or a great ellipse) is called a great arc. If X =
Curve
On converting relations to functions of several real variables
by F ( x , y ) = 0 {\displaystyle F(x,y)=0} can also be specified as the graph of a function f {\displaystyle f} , so that for each point ( x , y ) {\displaystyle
Implicit_function_theorem
Radius of the circle which best approximates a curve at a given point
reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius
Radius_of_curvature
Mathematical function relating circular and hyperbolic functions
function relates a hyperbolic angle measure ψ {\textstyle \psi } to a circular angle measure ϕ {\textstyle \phi } called the gudermannian of ψ {\textstyle
Gudermannian_function
Higher values of one variable leading to lower values of the other
between them is the cosine of the circular arc of separation of the points on a great circle of the sphere. When this arc is more than a quarter-circle (θ
Negative_relationship
Archimedean solid with 26 faces
not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane. Like many other solids the truncated octahedron has full
Truncated_cuboctahedron
Intermittent motion mechanism
producing a single-dwell: arc-based and linear-based. An arc-based single dwell linkage uses the approximation of a circular arc. The concept for linkage
Dwell_mechanism
Measure of distance in physical space
the sphere. In an unweighted graph, the length of a cycle, path, or walk is the number of edges it uses. In a weighted graph, it may instead be the sum
Length
C. Laskar (born 1932), Indian-American graph theorist, specialist in domination numbers and circular arc graphs Klavdiya Latysheva (1897–1956), Soviet
List_of_women_in_mathematics
radii of a circle Circular sector – Portion of a disk enclosed by two radii and an arc Circular segment – Area bounded by a circular arc and a straight line
List_of_circle_topics
Object in graph theory
for several other classes of graph, such as circular-arc graphs (as proven in Regan (2007)) and series-parallel graphs (as proven in Anderson et al.
Eternal_dominating_set
Algorithm in mathematical optimization
creating a residual graph, initializing the preflow values to zero and performing a set of saturating push operations on residual arcs (s, v) exiting the
Push–relabel maximum flow algorithm
Push–relabel_maximum_flow_algorithm
Mathematical measure of how much a curve or surface deviates from flatness
tangent vector, T. A section of a curve is also called an arc, and length along the curve is arc length, s. So the curvature for a small section of the curve
Curvature
Simple curve of Euclidean geometry
360 degrees, or one turn. Using radians, the formula for the arc length s of a circular arc of radius r and subtending a central angle of measure 𝜃 is
Circle
Euler's formula, e ix = cos x + i sin x Euler's polyhedral formula for planar graphs or polyhedra: v − e + f = 2, a special case of the Euler characteristic
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
Computer control of machine tools
system. This system is a typical plane often seen in mathematics when graphing. This system is required to map out the machine tool paths and any other
Computer_numerical_control
Graphic visual representation of information
are used to pull related nodes together. Arc diagrams are one-dimensional layouts of nodes with circular arcs linking each node. When used properly, with
Infographic
Algorithm for finding shortest paths
an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer
Dijkstra's_algorithm
Coordinates comprising a distance and an angle
then consists of points of the form (r(φ), φ) and can be regarded as the graph of the polar function r. Note that, in contrast to Cartesian coordinates
Polar_coordinate_system
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
Any planar graph can be subdivided by removing a few vertices
In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split
Planar_separator_theorem
Open-source visualization software package
Alluvial diagram Arc diagram Bar chart Multi-set bar chart Stacked bar chart Beeswarm plot Box plot Bumpchart Circle packing Dendrograms: Circular dendrogram
RAWGraphs
Separation between two points
arc length of the curve. The distance travelled may also be signed: a "forward" distance is positive and a "backward" distance is negative. Circular distance
Distance
Hyperbolic analogues of trigonometric functions
direct relationship between the circular functions and the hyperbolic functions that does not involve complex numbers. The graph of the function a cosh
Hyperbolic_functions
Plane curve: conic section
intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The graph of a quadratic function
Parabola
Field of mathematics dealing with three-dimensional Euclidean spaces
A lens (or less than half of a circular arc) rotated about an axis passing through the endpoints of the lens (or arc) Hyperboloid A surface that is generated
Solid_geometry
Relation between distances of four points
distances in this graph are not Ptolemaic. The graphs in which the distances obey Ptolemy's inequality are called the Ptolemaic graphs and have a restricted
Ptolemy's_inequality
Functions of an angle
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate
Trigonometric_functions
Vector graphics markup language developed by Digital Equipment Corporation
terminals. ReGIS supports rudimentary vector graphics consisting of lines, circular arcs, and similar shapes. Terminals supporting ReGIS generally allow graphics
ReGIS
Study of curves from a differential point of view
vectors double in length. The second graph shows the same spiral with its arc-length parametrization, –γ(s). The arc length of the first full turn is about
Differentiable_curve
Plane curve: conic section
definition of a hyperbola by its foci and its circular directrices (see above) can be used for drawing an arc of it with help of pins, a string and a ruler:
Hyperbola
Identifying translation relationships among the words in a bitext
multiword units) in a bitext, resulting in a bipartite graph between the two sides of the bitext, with an arc between two words if and only if they are translations
Bitext_word_alignment
Special labeling in graph theory
In graph theory, the act of coloring generally implies the assignment of labels to vertices, edges or faces in a graph. The incidence coloring is a special
Incidence_coloring
Atmospheric optical phenomenon
angle subtended at the eye of the observer. Outgoing ray angles (in the graphs on the right in the figure below) were obtained from the equation at the
22°_halo
In mathematics, straight line touching a plane curve without crossing it
mathematical smoothness, known as "differentiability." For example, if two circular arcs meet at a sharp point (a vertex) then there is no uniquely defined tangent
Tangent
Logic problem, AND of pairwise ORs
Kobourov, Stephen G. (2007), "Fixed-location circular arc drawing of planar graphs" (PDF), Journal of Graph Algorithms and Applications, 11 (1): 145–164
2-satisfiability
Largest verified impact structure on Earth
sediments (e.g. quartzites and banded ironstones), they form the prominent arc of hills that can be seen to the northwest of the impact structure's centre
Vredefort_impact_structure
Increasing sequence of reduced fractions
Comparison of Ford circles and a Farey diagram with circular arcs for n from 1 to 9. Each arc intersects its corresponding circles at right angles. In
Farey_sequence
Symbols for constants, special functions
reaction the angle that subtends the arc of a circular curve in surveying the maximum degree of any vertex in a given graph sensitivity to price in mathematical
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Curve from a cone intersecting a plane
can be used as alternative definitions. One such property defines a non-circular conic to be the set of those points whose distances to some particular
Conic_section
1 minus the cosine of an angle
Functions - Circular functions". In Abramowitz, Milton; Stegun, Irene Ann (eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical
Versine
Surface specified with parameters
simplest type of parametric surfaces is a bivariate surface, given by the graphs of functions of two variables (bivariate functions): z = f ( x , y ) , r
Parametric_surface
Four-dimensional analog of the dodecahedron
adjacency matrix of the vertices representing the polyhedral graph of the unit-radius 120-cell, the graph diameter is 15, connecting each vertex to its coordinate-negation
120-cell
Apparent force in a rotating reference frame
because this argument uses the Earth's rotating frame of reference. The graph shows that the Eötvös effect is not symmetrical, and that the resulting
Coriolis_force
Azimuthal equal-area map projection
intersects the hemisphere in a circular arc, called the trace of the plane, which projects down to a curve (typically non-circular) in the disk. One can plot
Lambert azimuthal equal-area projection
Lambert_azimuthal_equal-area_projection
Electrical engineers graphical calculator
Antenna Laboratory, University of California, Berkeley, California, USA. "Graph for Smith Chart" (PDF). electronics. Vol. 23, no. 1. New York, USA: McGraw-Hill
Smith_chart
Diffraction pattern in optics
descriptions of the best-focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is
Airy_disk
Branch of mathematics
line: it gives a way to quantify the steepness of the graph of a function, even when that graph is not a straight line. In Lagrange's notation, the symbol
Calculus
Algorithm to find Euclidean shortest paths
restricted to 2D grids. CWave - Uses geometric primitives (discrete circular arcs and lines) to represent the propagating wave front on the grid. For
Any-angle_path_planning
Set of points at distance less than one from a given point
set of points for the Poincaré disk model of the hyperbolic plane. Circular arcs perpendicular to the unit circle form the "lines" in this model. The
Unit_disk
Ringed dwarf planet in the Kuiper belt
formally announced by the Minor Planet Center in a Minor Planet Electronic Circular on 7 October 2002. It was given the provisional designation 2002 LM60,
Quaoar
Topological space that locally resembles Euclidean space
Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the
Manifold
Model of personality and behavior
and inflexible in their personal relationships might graph her personality somewhere on the arc between dominance and love. However, a person who exhibits
Interpersonal_circumplex
Class of map projections
refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie
Polyconic_projection_class
straight line, other meridians as complex curves, and parallels as circular arcs. Azimuthal In standard presentation, azimuthal projections map meridians
List_of_map_projections
Geometric drawing device
{\displaystyle C_{i}} , which (again in the absolute system) undergoes circular motion thus: x c = ( R − r ) cos t , y c = ( R − r ) sin t . {\displaystyle
Spirograph
Branch of physics describing the motion of objects without considering forces
{\text{d}}t} or Δ r {\displaystyle \Delta r} is the area under a velocity–time graph. We can take Δ r {\displaystyle \Delta r} by adding the top area and the
Kinematics
Equations that describe the behavior of a physical system
illustrated graphically by plotting velocity against time as a straight line graph. Algebraically, it follows from solving [1] for a = ( v − v 0 ) t {\displaystyle
Equations_of_motion
The graph is often attributed, for example the edges are marked as concave or convex. This graph is then analyzed to extract subsets of nodes and arcs that
Feature_recognition
CIRCULAR ARC-GRAPH
CIRCULAR ARC-GRAPH
Boy/Male
Indian, Sanskrit
Circular; Resembles a Wheel
Male
Icelandic
Icelandic form of Old Norse VÃðarr, VIÃAR means "forest warrior."
Boy/Male
Hindu
The Sun, Lightening, Fire, Hymn, A sage
Male
French
 Short form of French Marceau, MARC means "defense" or "of the sea." Compare with another form of Marc.
Boy/Male
Hindu
Lord vishnus weapon, Circular
Male
English
Variant spelling of English Eric, ARIC means "ever-ruler."
Male
English
English short form of Celtic Arthur, possibly ART means "bear-man." Compare with another form of Art.
Male
Norse
Contracted form of Old Norse Hróðgeirr, HRÓARR means "famous spear."
Male
Irish
Irish Gaelic name derived from the vocabulary word art, ART means "bear" and "champion." In Irish legend, this is the name of a son of Conn of the Hundred Battles. Compare with another form of Art.
Girl/Female
Indian
Ornament, Decoration
Boy/Male
Indian
Mountain
Male
Icelandic
Icelandic form of Old Norse Hróarr, HRÓAR means "famous spear."
Boy/Male
Tamil
Lord vishnus weapon, Circular
Male
Irish
Irish Gaelic form of Norman French Robert, ROIBÉARD means "bright fame."
Male
English
 Short form of English Arnold, ARN means "eagle power." Compare with another form of Arn.
Male
Finnish
 Pet form of Finnish Aaroni, ARI means "light-bringer." Compare with other forms of Ari.
Boy/Male
Indian, Sanskrit
Circular; Resembles a Wheel
Male
Irish
Irish Gaelic form of Old High German Ricohard, RISTÉARD means "powerful ruler."
Male
Scandinavian
 Variant spelling of Scandinavian Arne, ARN means "eagle power." Compare with another form of Arn.
Girl/Female
Indian
The Sun
CIRCULAR ARC-GRAPH
CIRCULAR ARC-GRAPH
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Awakened
Girl/Female
Gaelic
Powerful in battle.
Girl/Female
Indian
Thunderbolt, Lightning
Surname or Lastname
English
English : topographic name for someone who lived on a heath (Middle English hethe, Old English hǣð) or a habitational name from any of the numerous places, for example in Bedfordshire, Derbyshire, Herefordshire, Shropshire, and West Yorkshire, named with this word. The same word also denoted heather, the characteristic plant of heathland areas. This surname has also been established in Dublin since the late 16th century.
Girl/Female
Hindu, Indian
Dimples
Girl/Female
Muslim
Lotus, Water Lily, A flower
Boy/Male
Arabic
Taker of India
Boy/Male
Muslim
Guide
Girl/Female
Hindu, Indian
Life
Female
African
of God; or, of the spirit.
CIRCULAR ARC-GRAPH
CIRCULAR ARC-GRAPH
CIRCULAR ARC-GRAPH
CIRCULAR ARC-GRAPH
CIRCULAR ARC-GRAPH
a.
Adhering to a fixed circle of legends; cyclic; hence, mean; inferior. See Cyclic poets, under Cyclic.
n.
A portion of a curved line; as, the arc of a circle or of an ellipse.
n.
The quality or state of being circular; a circular form.
a.
A sleeveless cloak, cut in circular form.
n.
A curvature in the shape of a circular arc or an arch; as, the colored arc (the rainbow); the arc of Hadley's quadrant.
a.
Circular; illogical.
adv.
In a circular manner.
a.
Round; circular; spherical.
n.
An arch.
v. t.
To cause to pass from place to place, or from person to person; to spread; as, to circulate a report; to circulate bills of credit.
n.
A circular dance.
a.
In the form of, or bounded by, a circle; round.
a.
Nearly circular.
a.
Perfect; complete.
v. i.
To move circularly; to form a circle; to circulate.
a.
Addressed to a circle, or to a number of persons having a common interest; circulated, or intended for circulation; as, a circular letter.
n.
The apparent arc described, above or below the horizon, by the sun or other celestial body. The diurnal arc is described during the daytime, the nocturnal arc during the night.
a.
A circular letter, or paper, usually printed, copies of which are addressed or given to various persons; as, a business circular.
a.
repeating itself; ending in itself; reverting to the point of beginning; hence, illogical; inconclusive; as, circular reasoning.