Title: Colorings with Fractional Defect,
Abstract: Consider a coloring of a graph such that each vertex is assigned a fraction
of each color, with the total amount of colors at each vertex summing to $1$.
We define the fractional defect of a vertex $v$ to be the sum of the overlaps
with each neighbor of $v$, and the fractional defect of the graph to be the
maximum of the defects over all vertices. Note that this coincides with the
usual definition of defect if every vertex is monochromatic. We provide results
on the minimum fractional defect of $2$-colorings of some graphs.