Herbert Groetzsch and Jan Mycielski worked in the 50ies on the chromatology of triangle free graphs. Groetzsch’s 3 color theorem assures that planar triangle free graphs have chromatic number 3 or less. Mycielski defined an operation on graphs which preserves triangle free graphs and increases the chromatic number exactly by …
Coloring manifolds is a wonderful theme because it is not that well studied and so has many low hanging fruits. Here is an other one. For d-manifolds, the chromatic number is between d+1 and 2d+2 and a growth rate (3d+1)/2 is observed and reasonably conjectured upper bound. I started to …
Some update about recent activities: a new calculus course, the Cartan magic formula and some programming about the coloring algorithm.
