Complex sentence: One consequence of the stronger version of Wagner's theorem, for four-connected graphs is to characterize the graphs that do not have a "K" 5 minor, by showing that every such graph is either planar or it can be decomposed into simpler pieces.
Split into simpler sentences: One consequence of the stronger version of Wagner's theorem for four-connected graphs is to characterize the graphs that do not have a "K" 5 minor. The theorem can be rephrased as stating that every such graph is either planar or it can be decomposed into simpler pieces.