Resumen:

Inspired by the Four Colour Problem for planar graphs, Birkhoff introduced the chromatic polynomial to study colourings of a graph. In this talk, we discuss some recent developments in the study of the chromatic polynomial; from a multivariable generalization known as the chromatic symmetric function, to a homology theory for graphs whose Euler characteristic recovers the chromatic symmetric function. No prior knowledge of any of the above terminology is assumed.