Graph Theory

Should clarify that the example of De Grey is not planar in the technical sense of the word but rather what's known as a unit distance graph.

The Moser Spindle graph in the resources download is an example that cannot be 3-coloured.

A hexagon tiling of the plane with hexagons of diameter close to 1 but not bigger will give a 7-colouring.

Improvements scheduled per student: suggestions welcome, gtm1 lecture description has some improvements within, same with pst14, add picture of moser spindle, picture of 7 colouring, graph colouring topics,

Add exercise solution/discussion GTM 6,7

Add email correspondence.

The first 4 week schedule should suffice for most introductory courses on graph theory.

First week cover the PST14 lectures (first 4).

Do some exercises if you have time (start on ex1 and 2 from GTM ch1).

Second week cover GTM Ch1 Euler trails. Do exercises 1 and 2.

Third week present solutions to 1 and 2 and watch presentation on Traveling Salesman problem. NP vs P. Define Hamiltonian cycle and state Theorem 9.

Fourth week prove Theorem 9 about Hamiltonian cycles. Do more exercises from Ch1.

If you have more time say a school term or semester keep going with exercises.

Week 7 state kuatowski and planar graph results. Week 8 prove planar graph results.

From here many options are possible depending on the direction one wants to go: Colouring, Chromatic polynomials etc piques interest for us, there are also