(Contains joint work with Jan Goedgebeur and Jorik Jooken)

Abstract: This talk will introduce some of the ways computer-assisted methods can be used in graph theory, with a particular focus on extremal graph theory. In this area, one seeks graphs satisfying prescribed constraints while optimizing a graph parameter such as the number of vertices or edges. A central example is the cage problem, which asks for the smallest possible regular graph of a given degree and girth. We will then turn to a natural variant, the bi-regular cage problem, and describe algorithms for finding interesting graphs in this setting.