Episode 21 – Planar graphs

Let G be a connected plane graph with p vertices, q edges and r regions. Then p − q + r = 2. Episode 21 – Planar graphs ...
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Episode 21 – Planar graphs European section – Season 2

Episode 21 – Planar graphs

The three houses problem

House 1

House 2

House 3

Water

Gas

Elec

Episode 21 – Planar graphs

Planar and plane graphs

Plane

Planar

Episode 21 – Planar graphs

Non-planar

Regions of the plane

Episode 21 – Planar graphs

Theorem 1 : Euler’s formula

Let G be a connected plane graph with p vertices, q edges and r regions. Then p − q + r = 2.

Episode 21 – Planar graphs

Theorem 2

Let G be a connected plane graph with p vertices, q edges, where p ≥ 3. Then q ≤ 3p − 6.

Episode 21 – Planar graphs