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Circle packing theorem

The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible patterns of tangent circles among non-overlapping circles in the plane. A circle packing is a collection of circles whose union is connected and whose interiors are disjoint. The intersection graph of a circle packing, called a coin graph, is the graph…

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Theorem statement and proofs

Other properties

Triangulated packings of surfaces

Applications

Algorithmic aspects

History

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Circle packing theorem

Nodes197
Edges196
Triples451
Avg. degree1.99
Density0.010152
Components1

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Circle packing theorem

Top relations

related to References · 396
Circle packing theorem → Abbildung, Achilleas, ACM, ACM-SIAM Symposium, Aharonov, Akad, Alan, Alexander, Algorithms, American Mathematical Society, An, Andreev's, Andrey, André, Anna, Annales Academiæ Scientiarum Fennicæ, Annals, Année, Antonios, AOP590
related to Conformal mapping · 10
Circle packing theorem → Bernhard Riemann, By, Conformal, He, However, More, The, The Riemann, Thurston's, William Thurston
related to Random walks · 10
Circle packing theorem → Brownian, For, In, Instead, Johan Jonnason, Omega, One, Schramm, Several, The
related to Graph drawing · 9
Circle packing theorem → Achilleas Papakostas, Balázs Keszegh, Circle, Dömötör Pálvölgyi, Fáry's, In, János Pach, Seth Malitz, They
related to Triangulated packings of surfaces · 9
Circle packing theorem → Among, By, Euclidean, In, Instead, Robert Connelly, The, There, Zhen Zhang
related to Theorem statement and proofs · 8
Circle packing theorem → Andreev, As, If, It, Koebe, Möbius, The, Thurston
related to Generalizations · 7
Circle packing theorem → Euclidean, Here, If, In, Möbius, Riemannian, The
is a · 1
Circle packing theorem → useful tool for problems including conformal maps
has application · 1
Circle packing theorem → The

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Important terminology

circle packing circles packings graph planar displaystyle theorem graphs doi radii mr one 10 plane vertex geometry conformal tangent finite

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Circle packing theoremis auseful tool for problems including conformal maps0.90text
Circle packing theoremhas applicationThe0.60section
Circle packing theoremrelated to Conformal mappingThe Riemann0.60section
Circle packing theoremrelated to Conformal mappingBernhard Riemann0.60section
Circle packing theoremrelated to Conformal mappingConformal0.60section
Circle packing theoremrelated to Conformal mappingHowever0.60section
Circle packing theoremrelated to Conformal mappingWilliam Thurston0.60section
Circle packing theoremrelated to Conformal mappingMore0.60section
Circle packing theoremrelated to Conformal mappingThurston's0.60section
Circle packing theoremrelated to Conformal mappingHe0.60section
Circle packing theoremrelated to Conformal mappingBy0.60section
Circle packing theoremrelated to Conformal mappingThe0.60section

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