Math Simplified
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Math Simplified

Graph Theory 101: Why all Non-Planar Graphs Contain K₅ or K₃,₃

An intuitive explanation of Kuratowski’s Theorem and Wagner’s Theorem, with lots of diagrams!

A planar graph is one that can be drawn in a plane without any edges crossing. For example, the complete graph K₄ is planar, as shown by the “planar embedding” below.

All diagrams by author.

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Russell Lim

Russell Lim

I teach high school mathematics in Melbourne, Australia. I like thinking about interesting problems and learning new things.