  By prior work, there is a distributed algorithm that finds a maximal
fractional matching (maximal edge packing) in $O(\Delta)$ rounds, where
$\Delta$ is the maximum degree of the graph. We show that this is optimal:
there is no distributed algorithm that finds a maximal fractional matching in
$o(\Delta)$ rounds.
  Our work gives the first linear-in-$\Delta$ lower bound for a natural graph
problem in the standard model of distributed computing---prior lower bounds for
a wide range of graph problems have been at best logarithmic in $\Delta$.
