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On the Hamilton Cycle of the Hypercube
Key Engineering Materials, 2011Hypercube is one of the basic types of interconnection networks. In this paper, we use the concept of the Cartesian product graph to define the hypercube Qn, we study the relationship between the isomorphic graphs and the Cartesian product graphs, and we get the result that there exists a Hamilton cycle in the hypercube Qn.
Yan Zhong Hu, Hua Dong Wang
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Oriented hamilton cycles in digraphs
Journal of Graph Theory, 1995AbstractWe show that a directed graph of order n will contain n‐cycles of every orientation, provided each vertex has indegree and outdegree at least (1/2 + n‐1/6)n and n is sufficiently large. © 1995 John Wiley & Sons, Inc.
Roland Häggkvist, Andrew Thomason
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Getting a Directed Hamilton Cycle Two Times Faster
Combinatorics, probability & computing, 2011Consider the random graph process where we start with an empty graph on n vertices and, at time t, are given an edge et chosen uniformly at random among the edges which have not appeared so far.
Choongbum Lee, B. Sudakov, Dan Vilenchik
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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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1991
Abstract: "The edges of the complete graph K[subscript n] are coloured so that no colour appears no more than k times, k = [n/A 1n n], for some sufficiently large A. We show that there is always a Hamiltonian cycle in which each edge is a different colour. The proof technique is probabilistic."
Frieze, Reed, Bruce A.
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Abstract: "The edges of the complete graph K[subscript n] are coloured so that no colour appears no more than k times, k = [n/A 1n n], for some sufficiently large A. We show that there is always a Hamiltonian cycle in which each edge is a different colour. The proof technique is probabilistic."
Frieze, Reed, Bruce A.
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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 in a random tournament
Random Structures & Algorithms, 1995AbstractThe number of Hamilton cycles in a random tournament is asymptotically normally distributed.
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1985
The following extension of Dirac's Theorem is proved. If G is a non-hamiltonian graph with at least three vertices and p,q are a pair of natural numbers satisfying p+q = δ(G)+1, then K p,q ⊂ G c .
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The following extension of Dirac's Theorem is proved. If G is a non-hamiltonian graph with at least three vertices and p,q are a pair of natural numbers satisfying p+q = δ(G)+1, then K p,q ⊂ G c .
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The Complexity of the Hamilton Cycle Problem in Hypergraphs of High Minimum Codegree
Symposium on Theoretical Aspects of Computer Science, 2016Frederik Garbe, Richard Mycroft
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