Geometric Aspects of Graph Theory I

3.1. Characterizations of planar graphs:

Kuratowski, Euler's inequalities, others.

3.2. Embedding of planar graphs:

Fáry's and Koebe's theorems, Tutte's algorithm, Hopcroft-Tarjan's algorithm or Shih-Hsu's algorithm.

-- TD:

implementation of Schnyder's drawing, with applications to Geometric (Geographic) routing (code provided for Schnyder tree decomposition).

-- TD:

implementation of Tutte's algorithm + application to embedding of communication graphs in sensor networks?