A short proof of Kuratowski's graph planarity criterion
Yury Makarychev · Journal of Graph Theory · 1997
We present a new short combinatorial proof of the sufficiency part of the well-known Kuratowski's graph planarity criterion. The main steps are to prove that for a minor minimal non-planar graph G and any edge xy: (1) G-x-y does not contain θ-subgraph; (2) G-x-y is homeomorphic to the circle; (3) G is either K5 or K{3,3}. © 1997 John Wiley & Sons, Inc.