Math Simplified
Published in

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.

--

--

--

Simplified is a publication aiming at making mathematics accessible and enjoyable.

Recommended from Medium

Flex your Problem Solving Skills with this Viral Math Puzzle

Playing with Geometry — IMO 2021 Problem 4

Diagram of Problem 4 from the 2021 IMO (question described below). Segments AD, DT, TX, XA are shown in blue and segments CD, DY, YZ, ZC are shown in pink.

Math news: Reporters

The Multinomial Probability Distribution

Online Blackjack For Real Money App 2021

Live Blackjack

Little bit of Likelihoods

Math News Pilot

Prim’s Algorithm

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Russell Lim

Russell Lim

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

More from Medium

An Infinite Sequence from the 2022 European Girls Maths Olympiad (EGMO)

consecutive perfect squares are separated by consecutive odd numbers

Mathematics: Methods in Vectors

Euler’s Number: Intuitive Approach.

Challenge: Write Down All 4-Digit Palindromic Numbers Divisible By 42