# BPML: Combinatorics in the plane - Dr Johannes Carmesin

A Birmingham Popular Maths Lecture from Dr Johannes Carmesin.

A plane graph consists of a set of points in the two dimensional plane and some lines joining some pairs of these points in such a way that these lines do not cross. A well-known theorem in Graph Theory is that the set of points of every plane graph can be coloured with at most four colours such that adjacent points (those joined by a line) get different colours. A simple proof of this theorem has not been found yet. But can you prove that one can colour all plane graphs with 7 colours? In this talk, I will give an introduction to plane graphs, and provide an overview of various techniques, geometric as well as algebraic.

*We will be running the **Birmingham Popular Maths Lecture series** online for this academic year.*

*The lectures are open to all members of public and the University. Particularly suitable for those studying mathematics at A-level but we also welcome advanced GCSE students. Please register to attend the lecture. There will be time at the end for questions.*