منابع مشابه
Hamiltonian paths in Cayley graphs
The classical Lovász conjecture says that every connected Cayley graph is Hamiltonian. We present a short survey of various results in that direction and make some additional observations. In particular, we prove that every finite group G has a generating set of size at most log2 |G|, such that the corresponding Cayley graph contains a Hamiltonian cycle. We also present an explicit construction...
متن کاملHamiltonian cycles and paths in Cayley graphs and digraphs - A survey
Cayley graphs arise naturally in computer science, in the study of word-hyperbolic groups and automatic groups, in change-ringing, in creating Escher-like repeating patterns in the hyperbolic plane, and in combinatorial designs. Moreover, Babai has shown that all graphs can be realized as an induced subgraph of a Cayley graph of any sufficiently large group. Since the 1984 survey of results on ...
متن کاملCayley graphs of order 30p are Hamiltonian
Correspondence should be addressed to Dave Witte Morris, [email protected] Received 22 January 2011; Accepted 18 April 2011 Academic Editor: Cai Heng Li Copyright q 2011 E. Ghaderpour and D. W. Morris. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original w...
متن کاملHamilton-Connected Cayley Graphs on Hamiltonian Groups
We refer to the preceding theorem as the Chen–Quimpo theorem throughout the paper. Are there other families of groups which admit analogues of the Chen–Quimpo theorem? A natural direction in which to look is towards groups that are, in some sense, ‘almost’ abelian. The dihedral groups have been investigated [2]. Another family of groups, and the subject of this paper, is the family of Hamiltoni...
متن کاملHamiltonian paths on Platonic graphs
We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the 2-holed torus is topolog...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.02.018