Hatcher-Algebraic-Topology · Problem 2.2.24

Homology

Mathematics — Graph Theory · euler-characteristic

Problem

Suppose we build S2S^2 from a finite collection of polygons by identifying edges in pairs. Show that in the resulting CW structure on S2S^2 the 1-skeleton cannot be either of the two graphs shown, with five and six vertices. [This is one step in a proof that neither of these graphs embeds in R2\mathbb{R}^2.]

Related theory

Browse the problem library