I was looking at coloring a representation of a snark graph as a drawing with crossings. I colored the arcs with two rules: if two arcs meet at the same vertex they have a distinct color. If three arcs meet at a crossing they are all the same color or distinct.

Here is a coloring of a particular drawings of the Petersen graph.

http://yberman.com/foxsnark.png

But I am curious, has this coloring of graph drawings been studied?

Edit:

Snarks are connected, bridgeless cubic graphs which can't be edge colored in three colors. One reason they are important is because proving any instance of the cycle double cover conjecture reduces to solving it for a snark.

My coloring is related to the Fox 3-coloring of knots. https://en.m.wikipedia.org/wiki/Fox_n-coloring It's for knots (which have no vertices)

As with knots at most two edges cross at any point. I should have explicitly stated this.