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Chordal graphs are precisely the graphs that are both odd-hole-free and even-hole-free (see holes in graph theory). Every chordal graph is a strangulated graph, a graph in which every peripheral cycle is a triangle, because peripheral cycles are a special case of induced
Chord diagrams are conventionally visualized by arranging the objects in their order around a circle, and drawing the pairs of the matching as chords of the circle. The number of different chord diagrams that may be given for a set of 2 n {\displaystyle 2n} cyclically ordered objects is the double factorial ( 2 n − 1 ) ! ! {\displaystyle (2n ...
Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem).
Every cycle of length at least 6 has a chord connecting two vertices that are a distance > 1 apart from each other in the cycle.. In the mathematical area of graph theory, a chordal bipartite graph is a bipartite graph B = (X,Y,E) in which every cycle of length at least 6 in B has a chord, i.e., an edge that connects two vertices that are a distance > 1 apart from each other in the cycle.
The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | =, where r is the radius of the circle, and d is the distance between the center of the circle and the ...
English: Gray, blue, red, green, light green, black graph papers with 1 cm–0.5 cm–1 mm grids (page size: A4) in printable PDF format. Date 25 July 2013, 18:04:17
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
A chord diagram is a graphical method of displaying the inter-relationships between data in a matrix. The data are arranged radially around a circle with the relationships between the data points typically drawn as arcs connecting the data. The format can be aesthetically pleasing, making it a popular choice in the world of data visualization.
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