Vertex-minors: dense graphs from sparse graphs

Structural graph theory has traditionally focused on graph classes that are sparse (that is, only contain graphs with few edges). Lately, however, there has been an ongoing shift towards the dense setting. In the first half of the talk we discuss how vertex-minors fit into this paradigm. In the second half we show how to prove things about vertex-minors by reducing back to the "sparse setting". The key new result is a theorem about circuit decompositions in Eulerian group-labelled graphs. This is joint work with Jim Geelen and Paul Wollan.