  Coloring the arcs of biregular graphs was introduced with possible
applications to industrial chemistry, molecular biology, cellular neuroscience,
etc. Here, we deal with arc coloring in some non-bipartite graphs. In fact, for
$1<k\in\mathbb{Z}$, we find that the odd graph $O_k$ has an arc factorization
with colors $0,1,\ldots,k$ such that the sum of colors of the two arcs of each
edge equals $k$. This is applied to analyzing the influence of such arc
factorizations in recently constructed uniform 2-factors in $O_k$ and in
Hamilton cycles in $O_k$ as well as in its double covering graph known as the
middle-levels graph $M_k$.
