Some Topological Methods in Graph Coloring Theory

Attempts to solve the famous Four Color Problem led to fruitful discoveries and rich coloring theories. In this talk, some old and some recent applications of tools from topology to graph coloring problems will be presented. In particular, the following subjects will be treated: The use of Eulerʹs formula and local planarity conditions, Kempe equivalence, homotopy, winding number and its higher dimensional analogues.