I have a problem solving this question :
I need to prove that if i have a finite not directed graph that every vertex in him have an even degree, i can direct all of it edges in a way that the in degree of every vertex equals to its out degree.
I have tried to solve it by induction and didn't really succeded.
thank you.
If each vertex of graph $G$ has an even degree, then each connected component of $G$ is Eulerian graph, i. e. each component has a cycle that includes all edges of this component. Then you can direct each edge in order of traversing an Eulerian cycle of corresponding connected component.