  We consider single-conflict colorings, a variant of graph colorings in which
each edge of a graph has a single forbidden color pair. We show that for any
assignment of forbidden color pairs to the edges of a $d$-degenerate graph $G$
on $n$ vertices of edge-multiplicity at most $\log \log n$, $O(\sqrt{ d } \log
n)$ colors are always enough to color the vertices of $G$ in a way that avoids
every forbidden color pair. This answers a question of Dvo\v{r}\'ak, Esperet,
Kang, and Ozeki for simple graphs (Journal of Graph Theory 2021).

Combinatorics;Discrete Mathematics