The prism over a graph G is the Cartesian product of G with the complete graph $K_2$. A graph G is hamiltonian if there exists a spanning cycle in G, and G is prism-hamiltonian if the prism over G is hamiltonian.

Rosenfeld and Barnette (1973) [15] conjectured that every 3-connected planar graph is prism-hamiltonian. We construct a counterexample to the conjecture.

中文翻译：

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3连通平面图的棱镜-哈密顿性的反例

图G上的棱镜是G与完整图的笛卡尔积${ķ}_2$。一个图ģ是哈密尔顿如果存在在一个跨越周期ģ，和G ^是棱柱哈密顿如果棱镜超过ģ是哈密尔顿。

Rosenfeld and Barnette（1973）[15]推测，每个三连接平面图都是棱柱形哈密顿量。我们为这个猜想构造了一个反例。