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Polyhedral graphs without hamiltonian cycles

✍ Scribed by Hansjoachim Walther


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
309 KB
Volume
79
Category
Article
ISSN
0166-218X

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✦ Synopsis


There is a constructed sequence of polyhedral cyclically 5-connected cubic non-hamiltonian graphs having only 5-gons and 8-gons as faces.


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## Abstract A graph __G__ of order at least 2__n__+2 is said to be __n__‐extendable if __G__ has a perfect matching and every set of __n__ independent edges extends to a perfect matching in __G__. We prove that every pair of nonadjacent vertices __x__ and __y__ in a connected __n__‐extendable graph

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## Abstract A group Ξ“ is said to possess a hamiltonian generating set if there exists a minimal generating set Ξ” for Ξ“ such that the Cayley color graph __D__~Ξ”~(Ξ“) is hamiltonian. It is shown that every finite abelian group has a hamiltonian generating set. Certain classes of nonabelian groups are