# proof of Veblen’s theorem

The proof is very easy by induction on the number of elements of the set $E$ of edges. If $E$ is empty, then all the vertices have degree zero, which is even. Suppose $E$ is nonempty. If the graph contains no cycle, then some vertex has degree $1$, which is odd. Finally, if the graph does contain a cycle $C$, then every vertex has the same degree mod $2$ with respect to $E-C$, as it has with respect to $E$, and we can conclude by induction.

Title proof of Veblen’s theorem ProofOfVeblensTheorem 2013-03-22 13:56:51 2013-03-22 13:56:51 mathcam (2727) mathcam (2727) 4 mathcam (2727) Proof msc 05C38