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Let $G$ be a simple cubic 2-connected plane graph. For every $2$-factor $X$of $G$ having $n$-components there exists a simple hamiltonian plane graph $J\subset G^{2}$ such that $|E(J)|= |E(G)| + 2n -2$ and $\Delta(J) \leqslant 5$.

An extension of a cubic 2-connected plane graph G to a hamiltonian plane graph contained in G^{2}