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Episode 21 – Planar graphs European section – Season 2

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Episode 21 – Planar graphs

European section – Season 2

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The three houses problem

House 1 House 2 House 3

Water Gas Elec

Episode 21 – Planar graphs

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Planar and plane graphs

Plane Planar Non-planar

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Regions of the plane

Episode 21 – Planar graphs

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Theorem 1 : Euler’s formula

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

pq + r = 2 .

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Theorem 2

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

q3p − 6 .

Episode 21 – Planar graphs

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