Infinite induced-saturated graphs

A graph G is H-induced-saturated if G is H-free but deleting any edge or adding any edge creates an induced copy of H.There are non-trivial graphs H, such as P 4 , for which no finite Hinduced-saturated graph G exists.We show that for every finite graph H that is not a clique or an independent set, there always exists a countable H-induced-saturated graph.In fact, we show that a far stronger property can be achieved: there is a countably infinite H-free graph G such that any graph G G obtained by making a locally finite set of changes to G contains a copy of H.