Abstract
A graph G is called H-induced-saturated if G does not contain an induced copy of H, but removing any edge from G creates an induced copy of H and adding any edge of Gc to G creates an induced copy of H. Martin and Smith studied a related problem, and proved that there does not exist a P4-induced-saturated graph, where P4 is the path on 4 vertices. Axenovich and Csikós gave examples of families of graphs H for which H-induced-saturated graph G exists, and asked if there exists a Pn-induced-saturated graph when n≥5. Our aim in this short note is to show that there exists a P6-induced-saturated graph.
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