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...
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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...
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This paper is motivated by a method used for DNA sequencing by hybridization presented in [Jacek Blazewicz, Marta Kasprzak, Computational complexity of isothermic DNA sequencing by hybridization, Discrete Appl. Math. 154 (5) (2006) 718–729]. This paper presents a class of digraphs: the quasi-adjoint graphs. This class includes the ones used in the paper cited above. A polynomial recognition alg...
متن کاملHamiltonian cycles in cubic Cayley graphs: the 〈2,4k,3〉 case
It was proved by Glover and Marušič (J. Eur. Math. Soc. 9:775–787, 2007), that cubic Cayley graphs arising from groups G = 〈a, x | a2 = x = (ax)3 = 1, . . .〉 having a (2, s,3)-presentation, that is, from groups generated by an involution a and an element x of order s such that their product ax has order 3, have a Hamiltonian cycle when |G| (and thus also s) is congruent to 2 modulo 4, and have ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1983
ISSN: 0012-365X
DOI: 10.1016/0012-365x(83)90269-8