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arXiv · 1606.01693

Polyhedra with few 3-cuts are hamiltonian

Gunnar Brinkmann·Carol T. Zamfirescu
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Abstract

In 1956, Tutte showed that every planar 4-connected graph is hamiltonian. In this article, we will generalize this result and prove that polyhedra with at most three 3-cuts are hamiltonian. In 2002 Jackson and Yu have shown this result for the subclass of triangulations. We also prove that polyhedra with at most four 3-cuts have a hamiltonian path. It is well known that for each $k \ge 6$ non-hamiltonian polyhedra with $k$ 3-cuts exist. We give computational results on lower bounds on the order of a possible non-hamiltonian polyhedron for the remaining open cases of polyhedra with four or five 3-cuts.

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Gunnar Brinkmann, Carol T. Zamfirescu. 2016-06-06. Polyhedra with few 3-cuts are hamiltonian. https://arxiv.org/abs/1606.01693

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