Let G be a locally finite infinite graph and let I(G) be the set of ends of G. The Freudenthal compactification of G is the topological space |G| which is obtained from the usual topological space of ...

If true, the following conjecture of Thomassen [Th81] is a planarity criterion for a special class of graphs that involves only K 5. Recall that a planar graph on n vertices contains at most 3n-6 ...