Work

Infinite induced-saturated graphs

Year: 2026

Type: article

Abstract: 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 nontrivial graphs H , such as $P_4$ , for which no finite H -induced-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 $G'\ne G$ obtained by making a locally finite set of changes to G contains a copy of H .

Source: Canadian Journal of Mathematics

DOI: 10.4153/s0008414x26102132

Authors: Marthe Bonamy, Carla Groenland, Tom Johnston, Natasha Morrison, Alexander Scott