Graphs on Surfaces

This week, and the first week after break, we will be covering graphs on surfaces.

Slides

The morning lecture introduced the idea of surfaces by looking at a “video game world” and how they are typically a torus; we then possed a long term question of whether the video game designers could have done better and made an actual sphere.

Turning to graphs, we introduced the utilities problem, which we translated into asking whether $K_{3,3}$ was planar, we proved that it wasn’t, using the fact that is is Hamiltonian.