Randomly $C_n ∪ C_m$ 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 $H = C_n ∪ C_m, m ≠ n$, is discussed.