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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 $P_{n}$, butdeleting any edge of $G$ as well as adding to $G$ any edge of $G^{c}$ createssuch 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-saturatedgraphs. R\"{a}ty (2019) constructed such a graph for $n=6$, and Cho, Choi andPark (2019) later constructed such graphs for all $n=3k$ for $k \geq 2$. Weshow by a different construction that $P_{n}$-induced-saturated graphs existfor all $n \geq 6$, leaving only the case $n=5$ open.

$P_{n}$-induced-saturated graphs exist for all $n \geq 6$