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 |
---|---|
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 |