Hamiltonian properties of generalized pyramids. (English) Zbl 1236.05121

Zamfirescu, Carol T.; Zamfirescu, Tudor I.

Math. Nachr. 284, No. 13, 1739-1747 (2011).

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

Keywords:

pyramid; prism; polytope; Hamiltonian; traceable

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