Given a (finite, simple, undirected) graph $\mathcal{G} = (V, E)$, an edge binning associates each $e_{ij} \in E$ with one or the other of its vertices $v_i, v_j \in V$. Let $c_i$ be the number of edges associated with vertex $v_i$ in a given edge binning. Find an edge binning such that $\max_{v_i \in V}(c_i)$ is minimized.
Is this (or its dual) a well-known problem, or reducible to a well-known problem?
Edit:
The proper formal problem statement follows (derived from Asahiro 2009), with $d^+(u)$ denoting the outdegree of vertex $u$.
Minimum Maximum Outdegree: Given a finite, simple, undirected graph $\mathcal{G}= (V, E)$, find an orientation $\Lambda$ of $\mathcal{G}$ that minimizes $\max_{u \in V}[d^+_\Lambda(u)]$.
This can equivalently be stated in terms of indegree.
Note that Asahiro et al. primarily study the problem involving a weighted graph and weighted outdegree, which is generally NP-hard.
Best Answer
This problem is equivalent to the graph orientation problem also known as the graph balancing problem. One is given an undirected graph and has to give an orientation of the edges which minimizes the maximum out-degree. If this value is $k$, then the graph is called $k$-orientable. Here are some articles on the topic "Graph Orientation Algorithms to Minimize the Maximum Outdegree", and "A note on graph balancing problems with restrictions".