无立方顶点的多面体是棱-汉密尔顿多面体

Pub Date : 2024-02-19 DOI:10.1002/jgt.23078

Simon Špacapan

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摘要

图 G$G$ 上的棱是 G$G$ 与两个顶点上的完整图的笛卡尔积。如果 G$G$ 上的棱是哈密顿的，那么图 G$G$ 就是棱哈密顿的。我们证明了每一个最小阶数至少为四的多面体图（即三连平面图）都是棱-哈密顿图。

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Polyhedra without cubic vertices are prism-hamiltonian

The prism over a graph $G$ is the Cartesian product of $G$ with the complete graph on two vertices. A graph $G$ is prism-hamiltonian if the prism over $G$ is hamiltonian. We prove that every polyhedral graph (i.e., 3-connected planar graph) of minimum degree at least four is prism-hamiltonian.

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