Induced-saturated graphs exist for even cycles

Abstract

A graph $G$ is \emph{$H$-induced-saturated} if $G$ has no induced subgraph isomorphic to $H$ but changing the adjacency of an arbitrary pair of vertices in $G$ creates an induced copy of $H$. The existence problem for $H$-induced-saturated graphs had previously been settled when $H$ is a complete graph, a path, an odd cycle, or an even cycle of length at most $10$. In this paper, for every integer $q\ge 3$, we construct a $C_{2q+2}$-induced-saturated graph. Hence, induced-saturated graphs exist for all cycles, except for the cycle of length 3.