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Five-Colour Theorem and Beyond
In 1994, Carsten Thomassen published a beautiful simple proof confirming that every planar graph is 5-list-colourable. Another beautiful proof on a similar topic was given a few years later by Mike Albertson who proved that every precolouring of a set of vertices in a planar graph that are far apart from each other can be extended to a 5-colouring of the whole graph. After presenting these enlightening contributions, the speaker will discuss possible common generalizations of these results and report on some recent progress.