A cycle structure theorem for hamiltonian graphs
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In this article, it was shown that a graph is pancyclic if it contains a cycle of length l for every l such that 3 ≤ l ≤ n. This result can be used to show that three well-known hamiltonian degree conditions (due to Chvatal, Fan, and Bondy) actually imply that a (n − 1)-graph is essentially pancyclical.About:
This article is published in Journal of Combinatorial Theory, Series B.The article was published on 1988-08-01 and is currently open access. It has received 45 citations till now. The article focuses on the topics: Hamiltonian path & Bipartite graph.read more
Citations
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Advances on the Hamiltonian Problem – A Survey
TL;DR: This article is intended as a survey, updating earlier surveys in the area and contains material on closely related topics such as traceable, pancyclic and hamiltonian-connected graphs and digraphs.
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Updating the Hamiltonian problem—a survey
TL;DR: This article contains some material on related topics such as traceable, hamiltonian-connected and pancyclic graphs and digraphs, as well as an extensive bibliography of papers in the area.
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Weakly pancyclic graphs
TL;DR: In this article, it was shown that in many cases the requirements on a graph which ensure that it is weakly pancyclic are considerably weaker than those required for it to be pancyclically.
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Generalizations of Dirac’s theorem in Hamiltonian graph theory—A survey
TL;DR: A survey on some recent results on generalization of Dirac’s theorem on Hamiltonian graph theory.
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A generalization of Fan's condition for Hamiltonicity, pancyclicity, and Hamiltonian connectedness
TL;DR: A weakened version of Fan's condition for Hamiltonicity is shown to be sufficient for a 2-connected graph to be pancyclic (with a few exceptions).
References
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On Hamilton's ideals
TL;DR: In this paper, the best possible generalization of Dirac, Posa, and Bondy's necessary and sufficient conditions for a graph to be Hamiltonian was proved. But this generalization was only applicable to bipartite graphs.
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Pancyclic graphs II
J.A Bondy,A. W. Ingleton +1 more
TL;DR: In this article, it was shown that the Ore conditions for a graph to be Hamiltonian actually imply that the graph is either pancyclic or else is K n 2, n 2.
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New sufficient conditions for cycles in graphs
TL;DR: A new sufficient condition for a graph to be Hamiltonian is given that does not require that the closure of the graph should be complete, and so it is independent of the conditions given by Bondy and Chvatal.
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Pancyclic graphs and a conjecture of Bondy and Chvátal
E.F Schmeichel,S.L Hakimi +1 more
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The Geng-Hua Fan conditions for pancyclic or Hamilton-connected graphs
A. Benhocine,A. P. Wojda +1 more
TL;DR: It is proved that if G is 2-connected, α(G) ≤ n2 and G satisfies P( n−1) [resp. P(n)], then G is Hamiltonian with some exceptions.