Abstract:For a graph H, a graph G is H-induced-saturated if G does not contain an induced copy of H, but either removing an edge from G or adding a non-edge to G creates an induced copy of H. Depending on the graph H, an H-induced-saturated graph does not necessarily exist. In fact, Martin and Smith [11] showed that P 4 -induced-saturated graphs do not exist, where P k denotes a path on k vertices. Axenovich and Csikós [1] asked the existence of P k -induced-saturated graphs for k ≥ 5; it is easy to construct such grap… Show more
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