Results 291 to 300 of about 445,337 (327)
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Journal of Graph Theory, 2007
AbstractThe prism over a graph G is the Cartesian product G □ K2 of G with the complete graph K2. If G is hamiltonian, then G□K2 is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be an interesting relaxation of being hamiltonian.
Kaiser, Tomáš +4 more
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AbstractThe prism over a graph G is the Cartesian product G □ K2 of G with the complete graph K2. If G is hamiltonian, then G□K2 is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be an interesting relaxation of being hamiltonian.
Kaiser, Tomáš +4 more
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Neighborhood unions and hamilton cycles
Journal of Graph Theory, 1991AbstractLet G be a graph on n vertices and N2(G) denote the minimum size of N(u) ∪ N(v) taken over all pairs of independent vertices u, v of G. We show that if G is 3‐connected and N2(G) ⩾ ½(n + 1), then G has a Hamilton cycle. We show further that if G is 2‐connected and N2(G) ⩾ ½(n + 3), then either G has a Hamilton cycle or else G belongs to one of ...
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Hamilton Cycles in Oriented Graphs
Combinatorics, Probability and Computing, 1993It is shown that an oriented graph of order n whose every indegree and outdegree is at least cn is hamiltonian if c ≥ ½ − 2−15 but need not be if c < ⅜.
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Hamilton Cycles and Paths in Fullerenes
Journal of Chemical Information and Modeling, 2007AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.
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Hamilton Cycles in Random Regular Digraphs
Combinatorics, Probability and Computing, 1994We prove that almost every r-regular digraph is Hamiltonian for all fixed r ≥ 3.
Cooper, Colin +2 more
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The Hamilton‐Waterloo problem for Hamilton cycles and triangle‐factors
Journal of Combinatorial Designs, 2011AbstractIn this article, we consider the Hamilton‐Waterloo problem for the case of Hamilton cycles and triangle‐factors when the order of the complete graph Kn is even. We completely solved the problem for the case n≡24 (mod 36). For the cases n≡0 (mod 18) and n≡6 (mod 36), we gave an almost complete solution. © 2012 Wiley Periodicals, Inc. J.
Lei, Hongchuan, Shen, Hao
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Hamilton cycles in claw‐free graphs
Journal of Graph Theory, 1988AbstractBondy conjectured that if G is a k‐connected graph of order n such that magnified image for any (k + 1)‐independent set / of G, then the subgraph outside any longest cycle contains no path of length k − 1. In this paper, we are going to prove that, if G is a k‐connected claw‐free (K1,3‐free) graph of order n such that magnified image for any (k
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Hamilton cycles in plane triangulations
Journal of Graph Theory, 2002AbstractWe extend Whitney's Theorem that every plane triangulation without separating triangles is hamiltonian by allowing some separating triangles. More precisely, we define a decomposition of a plane triangulation G into 4‐connected ‘pieces,’ and show that if each piece shares a triangle with at most three other pieces then G is hamiltonian.
Jackson, Bill, Yu, Xingxing
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