Journal ArticleDOI
Bipartite graphs with cycles of all even lengths
TLDR
It is proved here that this condition on the vertex degrees of X and Y implies that G contains cycles of every even length when n > 3.Abstract:
Let G = (X, Y, E) be a bipartite graph with X = Y = n. Chvatal gave a condition on the vertex degrees of X and Y which implies that G contains a Hamiltonian cycle. It is proved here that this condition also implies that G contains cycles of every even length when n > 3.read more
Citations
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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.
Journal ArticleDOI
Cycles and paths of many lengths in bipartite digraphs
Denise Amar,Yannis Manoussakis +1 more
TL;DR: Several sufficient conditions on the half-degrees of a bipartite digraph are given for the existence of cycles and paths of various lengths.
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Tight cycles and regular slices in dense hypergraphs
TL;DR: In this article, the authors study properties of random subcomplexes of partitions returned by Strong Hypergraph Regularity Lemma, which they call regular slices, and advocate their use in extremal hypergraph theory, and explain how they can lead to considerable simplifications in existing proofs.
Journal ArticleDOI
Extending cycles in bipartite graphs
TL;DR: It is shown that if σ (G) ≧ n + 1 and C is a 2 k -cycle in G then C is extendable unless 〈 V ( C )〉 ≅ K k , k .
References
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Journal ArticleDOI
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 and a conjecture of Bondy and Chvátal
E.F Schmeichel,S.L Hakimi +1 more