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|
|Date of creation||2013-03-22 13:56:51|
|Last modified on||2013-03-22 13:56:51|
|Last modified by||mathcam (2727)|