Prove that every graph $G$ with minimum degree $2m$ will have a bipartite subgraph having minimum degree $m$.
I have tried this proof by first taking one vertex $v$ and consider it in set $D_0$. Then i am taking m of its neighbours (out of $2m$) to form a set $D_1$. My main intension is to partition all vertex in G into $D_i$ s and create two partitions with $i$s as even in one partiotion and $i$s as odd in another partition.
But i am having a difficulty in proving that no edge exists between two $D_i$ in different levels