  Let $P_{n}$ be a path graph on $n$ vertices. We say that a graph $G$ is
$P_{n}$-induced-saturated if $G$ contains no induced copy of $P_{n}$, but
deleting any edge of $G$ as well as adding to $G$ any edge of $G^{c}$ creates
such a copy. Martin and Smith (2012) showed that there is no
$P_{4}$-induced-saturated graph. On the other hand, there trivially exist
$P_{n}$-induced-saturated graphs for $n=2,3$. Axenovich and Csik\'{o}s (2019)
ask for which integers $n \geq 5$ do there exist $P_{n}$-induced-saturated
graphs. R\"{a}ty (2019) constructed such a graph for $n=6$, and Cho, Choi and
Park (2019) later constructed such graphs for all $n=3k$ for $k \geq 2$. We
show by a different construction that $P_{n}$-induced-saturated graphs exist
for all $n \geq 6$, leaving only the case $n=5$ open.
