  The line graph of a graph $G$ is the graph $L(G)$ whose vertex set is the
edge set of $G$ and there is an edge between $e,f\in E(G)$ if $e$ and $f$ share
an endpoint in $G$. A graph is called line graph if it is a line graph of some
graph. We study the Line-Graph-Edge Deletion problem, which asks whether we can
delete at most $k$ edges from the input graph $G$ such that the resulting graph
is a line graph. More precisely, we give a polynomial kernel for
Line-Graph-Edge Deletion with $\mathcal{O}(k^{5})$ vertices. This answers an
open question posed by Falk H\"{u}ffner at Workshop on Kernels (WorKer) in
2013.
