  The Graph Minor Theorem of Robertson and Seymour asserts that any graph
property, whatsoever, is determined by an associated finite list of graphs. We
view this as an impressive generalization of Kuratowski's theorem, which
characterizes planarity in terms of two forbidden subgraphs, $K_5$ and
$K_{3,3}$. Robertson and Seymour's result empowers students to devise their own
Kuratowski type theorems; we propose several undergraduate research projects
with that goal. As an explicit example, we determine the seven forbidden minors
for a property we call strongly almost--planar (SAP). A graph is SAP if, for
any edge $e$, both deletion and contraction of $e$ result in planar graphs.
