Kuratowski-type theorems do not extend to pseudosurfaces (Q1193562)

The ``banana surface'' \(B_ 2\) is a pseudosurface obtained from two disjoint 2-spheres \(S\) and \(S'\) with distinguished points \(u\neq v\) in \(S\) and \(u'\neq v'\) in \(S'\) by identifying \(u\) with \(u'\) and \(v\) with \(v'\). The authors construct an infinite sequence \(H_ n\), \(n\geq 3\), of graphs such that \(H_ n\) does not embed in \(B_ 2\) but every proper subgraph of \(H_ n\) does. This shows that there are infinitely many forbidden graphs for \(B_ 2\) and that graph embeddability in pseudosurfaces cannot be characterized, in general, in terms of a finite set of forbidden graphs.