Discrete Math › Section C · Graph theory › Topic C.4
Planar graphs
Can a circuit be printed on a board without any wires crossing? Can three houses each be piped to three utilities without pipes crossing? Questions like these ask whether a graph is planar, and one short formula of Euler's answers many of them.
In this topic
- Drawings without crossings
- Faces
- Euler's formula
- Why Euler's formula holds
- Worked example: using the formula
- Too many edges to be planar
- Worked example: K5 and K3,3
- Kuratowski's theorem
- Worked example: why a football has 12 pentagons
- Polyhedra and the five regular solids
- Common mistakes to avoid
- Key takeaways
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