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.