  A matchstick graph is a crossing-free unit-distance graph in the plane.
Harborth (1981) proposed the problem of determining whether there exists a
matchstick graph in which every vertex has degree exactly $5$. In 1982,
Blokhuis gave a proof of non-existence. A shorter proof was found by Kurz and
Pinchasi (2011) using a charging method. We combine their method with the
isoperimetric inequality to show that there are $\Omega(\sqrt{n})$ vertices in
a matchstick graph on $n$ vertices that are of degree at most $4$, which is
asymptotically tight.
