scholarly journals Circle packings, kissing reflection groups and critically fixed anti-rational maps

2022 ◽  
Vol 10 ◽  
Author(s):  
Russell Lodge ◽  
Yusheng Luo ◽  
Sabyasachi Mukherjee
Keyword(s):  
Planar Graphs ◽  
Rational Maps ◽  
Reflection Groups ◽  
Circle Packings

Abstract In this article, we establish an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps. The correspondence, which is expressed using simple planar graphs, has several dynamical consequences. As an application of this correspondence, we give complete answers to geometric mating problems for critically fixed anti-rational maps.

scholarly journals Boundaries of planar graphs, via circle packings

2016 ◽  
Vol 44 (3) ◽  
pp. 1956-1984 ◽  
Author(s):  
Omer Angel ◽  
Martin T. Barlow ◽  
Ori Gurel-Gurevich ◽  
Asaf Nachmias
Keyword(s):  
Planar Graphs ◽  
Circle Packings

Harmonic functions on planar and almost planar graphs and manifolds, via circle packings

1996 ◽  
Vol 126 (3) ◽  
pp. 565-587 ◽  
Author(s):  
Itai Benjamini ◽  
Oded Schramm
Keyword(s):  
Harmonic Functions ◽  
Planar Graphs ◽  
Circle Packings

scholarly journals Balanced Circle Packings for Planar Graphs

2014 ◽  
pp. 125-136 ◽  
Author(s):  
Md. Jawaherul Alam ◽  
David Eppstein ◽  
Michael T. Goodrich ◽  
Stephen G. Kobourov ◽  
Sergey Pupyrev
Keyword(s):  
Planar Graphs ◽  
Circle Packings

Acute Constraints in Straight-Line Drawings of Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 994-1001
Author(s):  
Akane SETO ◽  
Aleksandar SHURBEVSKI ◽  
Hiroshi NAGAMOCHI ◽  
Peter EADES
Keyword(s):  
Planar Graphs ◽  
Line Drawings ◽  
Straight Line

A Space-Efficient Separator Algorithm for Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 1007-1016 ◽  
Author(s):  
Ryo ASHIDA ◽  
Sebastian KUHNERT ◽  
Osamu WATANABE
Keyword(s):  
Planar Graphs

Note on (semi-)proper orientation of some triangulated planar graphs

2021 ◽  
Vol 392 ◽  
pp. 125723
Author(s):  
Ruijuan Gu ◽  
Hui Lei ◽  
Yulai Ma ◽  
Zhenyu Taoqiu
Keyword(s):  
Planar Graphs ◽  
Proper Orientation

scholarly journals Integrable and Chaotic Systems Associated with Fractal Groups

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 237
Author(s):  
Rostislav Grigorchuk ◽  
Supun Samarakoon
Keyword(s):  
Operator Algebras ◽  
Probabilistic Approach ◽  
Schur Complement ◽  
Automata Theory ◽  
Random Schrödinger Operators ◽  
Rational Maps ◽  
Holomorphic Dynamics ◽  
Von Neumann ◽  
Intermediate Growth ◽  
Quasi Crystals

Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 1980s with the purpose of solving some famous problems in mathematics, including the question of raising to von Neumann about non-elementary amenability (in the association with studies around the Banach-Tarski Paradox) and John Milnor’s question on the existence of groups of intermediate growth between polynomial and exponential. Fractal groups arise in various fields of mathematics, including the theory of random walks, holomorphic dynamics, automata theory, operator algebras, etc. They have relations to the theory of chaos, quasi-crystals, fractals, and random Schrödinger operators. One important development is the relation of fractal groups to multi-dimensional dynamics, the theory of joint spectrum of pencil of operators, and the spectral theory of Laplace operator on graphs. This paper gives a quick access to these topics, provides calculation and analysis of multi-dimensional rational maps arising via the Schur complement in some important examples, including the first group of intermediate growth and its overgroup, contains a discussion of the dichotomy “integrable-chaotic” in the considered model, and suggests a possible probabilistic approach to studying the discussed problems.

scholarly journals Distributed Dominating Set Approximations beyond Planar Graphs

2019 ◽  
Vol 15 (3) ◽  
pp. 1-18 ◽  
Author(s):  
Saeed Akhoondian Amiri ◽  
Stefan Schmid ◽  
Sebastian Siebertz
Keyword(s):  
Planar Graphs ◽  
Dominating Set
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