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

Abstract

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 $\Delta (J)⩽5$.

arXiv comment5 pages, 2 figures