Planarity Algorithm (Edexcel A-Level Further Mathematics): Flashcards

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Planarity Algorithm
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Definition of a planar graph

A graph drawable on a plane without edges crossing

Hamiltonian cycle

Cycle visiting every vertex exactly once, returning to start

Kuratowski's Theorem: condition for non-planarity

Contains subgraph homeomorphic to K5K_5 or K3,3K_{3,3}

What is K5K_5?

Complete graph on 5 vertices

What is K3,3K_{3,3}?

Complete bipartite graph with two sets of 3 vertices

Euler's formula for planar graphs

v−e+f=2v - e + f = 2

In Euler's formula, what does vv represent?

Number of vertices

In Euler's formula, what does ee represent?

Number of edges

In Euler's formula, what does ff represent?

Number of faces (including outer face)

How many edges does K5K_5 have?

10 edges

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