Randomly $C_{n} \cup C_{m}$ graphs

Abstract

A graph $G$ is said to be a randomly $H$ graph if and only if any subgraph of $G$ without isolated vertices, which is isomorphic to a subgraph of $H$, can be extended to a subgraph $F$ of $G$ such that $F$ is isomorphic to $H$. In this paper the problem of randomly $H$ graphs, where $H = C_{n} \cup C_{m}$, $m \neq n$, is discussed.