×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aldred, Nonhamiltonian 3-connected cubic planar graphs, SIAM J. Discrete Math. 13 (1) pp 25– (2000) · Zbl 0941.05041 · doi:10.1137/S0895480198348665
[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 · doi:10.1002/jgt.3190090311
[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 · doi:10.4153/CMB-2009-045-6
[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.