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**Hamiltonian properties of generalized pyramids.**
*(English)*
Zbl 1236.05121

A polytope is called a \(k\)-pyramid if it has at most \(k\) pairwise disjoint facets, called bases such that every other facet has some neighbouring base. A \(k\)-pyramid is belted if some pair of bases has no common neighbouring facet. A polytope in \(R^3\) is hamiltonian (traceable) if its \(1\)-skeleton has a hamiltonian cycle (path). It is shown that every \(2\)-pyramid is traceable (but not necessarily hamiltonian), and every non-belted \(3\)-pyramid is traceable. It is also shown that a non-belted \(2\)-pyramid is hamiltonian. Other hamiltonian and traceable results for special \(2\)-pyramids and \(3\)-pyramids are proved.

Reviewer: Ralph Faudree (Memphis)

### MSC:

05C45 | Eulerian and Hamiltonian graphs |

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\textit{C. T. Zamfirescu} and \textit{T. I. Zamfirescu}, Math. Nachr. 284, No. 13, 1739--1747 (2011; Zbl 1236.05121)

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### References:

[1] | Aldred, Nonhamiltonian 3-connected cubic planar graphs, SIAM J. Discrete Math. 13 (1) pp 25– (2000) · Zbl 0941.05041 |

[2] | Bondy, Infinite and Finite Sets, Vol. 10 pp 181– (1975) · Zbl 0324.05110 |

[3] | Bondy, Lengths of cycles in Halin graphs, J. Graph Theory 8 pp 397– (1985) · Zbl 0587.05039 |

[4] | Grinberg, Latvian Math Vol. 4 pp 51– (1968) |

[5] | Malik, Hamiltonian properties of generalized Halin graphs, Can. Math. Bull. 52 (3) pp 416– (2009) · Zbl 1171.05031 |

[6] | Skowrońska, Hamiltonian properties of Halin-like graphs, Ars Comb. 16-B pp 97– (1983) |

[7] | Skowrońska, Hamiltonian cycles in skirted trees, Zastosow. Mat. 19 (3-4) pp 599– (1987) · Zbl 0719.05045 |

[8] | Skupień, Contemporary Methods in Graph Theory pp 537– (1990) |

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