## 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.

### MSC:

 05C45 Eulerian and Hamiltonian graphs

### Keywords:

pyramid; prism; polytope; Hamiltonian; traceable
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### References:

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