Hey guy i am soooo stuck on this question any help would be greatly appreciated!!

Let G be a 9-regular graph with vertices and suppose has the property that any subgraph with more that edges has a vertex of degree at least 2. Prove that there is a subgraph of with the property that if the vertices of and all the edges incident with the vertices of are removed from , then what remains is a graph with more than components of odd order.