Circle Representation of Planar Graphs: A Polyhedral Approach

DESCRIPTION

Explore Koebe's concept from 1936 that every planar graph can be represented using touching circles. Andre'ev's theory connects polyhedra to the dual disc representation, creating a bridge between graphs and horizons. Dive into the world of dual disc representations and convex polytopes.

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Mar 18, 2014

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Circle Representation of Planar Graphs: A Polyhedral Approach

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Disc representation Koebe (1936) Every planar graph can be represented by touching circles
Polyhedral version Every 3-connected planar graph is the skeleton of a convex polytope such that every edge touches the unit sphere Andre’ev
From polyhedra to circles horizon
From polyhedra to representation of the dual
disc representation disc representation graph dual horizon