I'm very stuck with this problem. Given $G = (V, E, A)$ a mixed graph where every edge in $E$ is directed and every edge in $A$ is undirected. Thinking as a max-flow problem, decide if it's possible to give a direction to every $a \in A$ in order to make $G$ an $eulerian$ graph.
The model I've thinking so far is to translate the problem as a matching problem. For every non directed edge, I would like to determine to which node this will point. For example, if $e=(u,v)$, from the vertex source there should be an edge connecting to $e$ and this one will be connected to $u$ and $v$. Every edge will have a flow capacity of 1, except for the edges of the target, which will have a capacity of $?$. I don't know if this model it's okay, but any clue (or another model) will help, thanks!