proof of Veblen’s theorem

The proof is very easy by inductionMathworldPlanetmath 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
Canonical name ProofOfVeblensTheorem
Date of creation 2013-03-22 13:56:51
Last modified on 2013-03-22 13:56:51
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 4
Author mathcam (2727)
Entry type Proof
Classification msc 05C38