Minors in partial cubes

We will define and motivate a minor relation in the family of partial cubes. The main topic of the talk will be the forbidden minors characterizations of well established subfamilies. We will present new results on the family of partial cubes that have no forbidden minor isomorphic to a 3-dimensional hypercube minus a vertex. This family plays an important role in understanding bipartite graphs and in establishing a hierarchy among its subfamilies.