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Circle Representation of Planar Graphs: A Polyhedral Approach

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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Circle Representation of Planar Graphs: A Polyhedral Approach

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  1. Disc representation Koebe (1936) Every planar graph can be represented by touching circles

  2. Polyhedral version Every 3-connected planar graph is the skeleton of a convex polytope such that every edge touches the unit sphere Andre’ev

  3. From polyhedra to circles horizon

  4. From polyhedra to representation of the dual

  5. disc representation disc representation graph dual horizon

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