Apollonian network is an undirected graph formed by a process of recursively subdividing a triangle into three smaller triangles. Apollonian networks...

In mathematics, an Apollonian gasket, Apollonian net, or Apollonian circle packing is a fractal generated by starting with a triple of circles, each tangent...

the maximal outerplanar graphs. Planar 3-trees are also known as Apollonian networks. The graphs that have treewidth at most k are exactly the subgraphs...

This is the only counterexample.[citation needed] Mathematics portal Apollonian network Five color theorem Graph coloring Grötzsch's theorem: triangle-free...

the graphs of three-dimensional stacked polyhedra are exactly the Apollonian networks, the graphs formed from a triangle by repeatedly subdividing a triangular...

The uniquely 4-colorable planar graphs are known to be exactly the Apollonian networks, that is, the planar 3-trees. Every connected bipartite graph is...

mathematician and astronomer – Apollonian circles, Apollonian gasket, Apollonian network, Apollonius' theorem, Problem of Apollonius Saint Thomas Aquinas,...

at most two, and the Apollonian networks have degeneracy three. The Barabási–Albert model for generating random scale-free networks is parameterized by...

is a chordal graph. As a planar 3-tree, it forms an example of an Apollonian network. By Steinitz's theorem, the Goldner–Harary graph is a polyhedral graph:...

Delauney triangularization from piecewise linear data Subdivisions: Apollonian network — undirected graph formed by recursively subdividing a triangle Barycentric...

with v > 2, then it has precisely 3v − 6 edges and 2v − 4 faces. Apollonian networks are the maximal planar graphs formed by repeatedly splitting triangular...

maximal cliques and all maximal clique separators have the same size. Apollonian networks are chordal maximal planar graphs, or equivalently planar 3-trees...

(realizations of prism graphs), and stacked polyhedra (realizations of Apollonian networks). Another way of stating the existence of integer realizations is...

pseudoforests, series–parallel graphs, outerplanar graphs, Halin graphs, and Apollonian networks. The control-flow graphs arising in the compilation of structured...

pseudoforests, series–parallel graphs, outerplanar graphs, Halin graphs, and Apollonian networks. For instance, the series–parallel graphs are a subfamily of the...

bounding the disk. Orthogonality Radical axis Power center (geometry) Apollonian circles Bipolar coordinates Chaplick, Steven; Förster, Henry; Kryven,...

precisely means that the point x i {\displaystyle x_{i}} falls between two Apollonian spheres. T. Kohonen. Self-Organizing Maps. Springer, Berlin, 1997. T....

list of dynamical systems and differential equations topics. 1/f noise Apollonian gasket Attractor Box-counting dimension Cantor distribution Cantor dust...

of curves and the caustic of a given curve. In machine learning, neural networks are families of curves with parameters chosen by an optimization algorithm...

Loans, Big Promises, Unknown Impact: An Examination of Microfinance". The Apollonian Revolt. Archived from the original on 28 July 2015. Retrieved 31 July...

Shindler, Michael. "A Criticism of Putnam's Theory of Social Capital". The Apollonian Revolt. Archived from the original on 19 April 2015. Retrieved 6 April...

and Animal Logic's work were heavily based on fractal art, including Apollonian gaskets and Mandelbulbs, and was described by director James Gunn as "the...

Epic, cited by R. F. Glei, Outlines of Apollonian Scholarship 1955–1999, 11 R. F. Glei, Outlines of Apollonian Scholarship 1955–1999, p. 5 A. Rose, Three...

close collaborators. Its main defining features in poetry are a return to Apollonian classicism, a very refined and accurate language, objectivity and rejection...

by Friedrich Nietzsche, whose views on aesthetics, morality, and the Apollonian and Dionysian duality would appear in his conversation, poetry, and songs...

German philosopher Friedrich Nietzsche proposed that a tension between Apollonian and Dionysian aesthetic principles underlay the development of Greek tragedy;...

the Monstrous Ego of 'Guardians of the Galaxy Vol. 2'". Animation World Network. Archived from the original on October 26, 2018. Retrieved June 22, 2017...

as to experience a revealing dream), the Kliromanteion and finally the Apollonian, with the laurel. But ever since the introduction of the cult of Dionysus...

exchange, validation of coinage, and loans. The first treasury to the Apollonian temple was built before the end of the 7th century BCE. A treasury of...

the mid-fifth century the Apollonians expanded toward the Bay of Valona, conquering the city of Thronium. ... The Apollonian inscription speaks of booty...