Is there an English translation of Kuratowski's theorem on forbidden minors of planar graphs? Is there an English translation of Kuratowski's proof about planar graphs?
 A: Kuratowski's theorem is set as an exercise in Ch. 5 of Combinatorial Problems and Exercises by Lovasz. The problem is given as follows:
Let G be a minimal non-planar graph with all vertices of degree at least 3. Then:


*

*G is 3-connected. (This is straightforward; supposing otherwise and removing the cutset we can get a planar embedding of G.)

*G contains a cycle with a chord. (Provided hint: Consider a maximum path.)

*G is isomorphic to one of $K_5$, $K_{3, 3}$.

*Conclude Kuratowski's theorem from part 3.


The proof is on pp. 299-301, which fortunately are all viewable in the Google Books preview.
A: In case you are asking for the original paper "Sur le problème des courbes gauches en Topologie" by Kuratowski where he first proves his characterization of planar graphs, then a translation by J.Jaworowski can be found in "Graph Theory, Łagów", 1981, M. Borowiecki, J. W. Kennedy and M. M. Sysło. It is the proceedings of a conference held in Łagów, dedicated to the memory of K.Kuratowski.
A: You might just want to read Jim Belk's excellent exposition at the Everything Seminar.
