Given a simple Graph $G=(V,E)$ ($V$ vertices, $E$ edges) I have to show that there exists a distribution $V= V_1 \cup V_2$ of the vertices such that all vertices in the induced subgraphs $G[V_1]$ and $G[V_2]$ have even degree.
I honestly have no idea how to solve this question. I tried several things (which I will list below) but all attempts have failed.
induction: Induction on the number of vertices has proven to be extremely ugly for this question, so I dropped the idea really quick.
color all circles with odd elements first.
use that in $G$ there is an even amount of vertices with odd degree.
I do not want a complete answer to this question (at least not for the moment). Does anyone have an idea/tip for this question which doesn't give away too much?
I hope you can help me
slinshady
