proof of Veblen’s theorem
The proof is very easy by induction
on the number of elements of
the set of edges.
If is empty, then all the vertices have degree zero, which is even.
Suppose is nonempty.
If the graph contains no cycle, then some vertex has degree , which is odd.
Finally, if the graph does contain a cycle , then every vertex has
the same degree mod with respect to , as it has with respect
to , 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 |