All Questions
Tagged with circle-packing graph-theory
7 questions
4
votes
1
answer
225
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Harmonic functions as limits of harmonic functions on graphs?
I have recently learned about Rodin and Sullivan's work that proved a conjecture of Thurston involving giving a construction for the map in the Riemann mapping theorem using circle packings and this ...
- 1,075
16
votes
4
answers
1k
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Squaring a square and discrete Ricci flow
Is this a theorem?
Every $3$-connected planar graph $G$ may be represented as
a tiling of a square by squares,
one square per node of $G$, with nodes connected in $G$
corresponding to tangent squares....
- 151k
10
votes
2
answers
1k
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Proofs of circle packing theorem
Circle packing theorem is a famous result stating that for every connected simple planar graph $G$ there is a circle packing in the plane whose intersection graph is $G$ https://en.wikipedia.org/wiki/...
- 14.3k
1
vote
0
answers
254
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Interior and boundary vertices of weighted graphs
Xu He's article Rigidity of Infinite Disk Patterns and I have a problem with a statement he makes on page 7.
He considers weighted embedded planar graphs $G=(V, E)$ with weight function $\Theta: E \...
- 81
1
vote
0
answers
87
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Are morphisms of intersection graphs of circle packings harmonic?
Let $P$ and $Q$ be circle packings on compact Riemann surfaces (along with some Riemannian metrics) $X$ and $Y$. Let $f\colon X\to Y$ be a conformal map taking each circle in $P$ to a circle in $Q$. ...
- 3,079
2
votes
0
answers
246
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A primal-dual (double) circle packing (coin graph) question
I know that any 3-connected simple planar graph with a designated outside face (outer face) has a primal-dual (double) circle packing (Brightwell-Scheinerman Theorem).
Q1- But I am not sure whether ...
- 415
4
votes
1
answer
467
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Generalizing the circle packing theorem to 3-dimensions
The circle packing theorem (Koebe–Andreev–Thurston theorem) states that every finite planar graph is the nerve of some disk packing in the plane, where the nerve of a packing $P$ is a graph $G=(V,E)$, ...
- 1,431