On Hamiltonian properties of powers of special Hamiltonian graphs
Gary Chartrand, S. F. Kapoor (1974)
Colloquium Mathematicae
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Gary Chartrand, S. F. Kapoor (1974)
Colloquium Mathematicae
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Kewen Zhao, Ronald J. Gould (2010)
Colloquium Mathematicae
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An independent set S of a graph G is said to be essential if S has a pair of vertices that are distance two apart in G. In 1994, Song and Zhang proved that if for each independent set S of cardinality k+1, one of the following condition holds: (i) there exist u ≠ v ∈ S such that d(u) + d(v) ≥ n or |N(u) ∩ N(v)| ≥ α (G); (ii) for any distinct u and v in S, |N(u) ∪ N(v)| ≥ n - max{d(x): x ∈ S}, then G is Hamiltonian. We prove that if for each...
Zhao, Kewen (2011)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: 05C38, 05C45. In 1952, Dirac introduced the degree type condition and proved that if G is a connected graph of order n і 3 such that its minimum degree satisfies d(G) і n/2, then G is Hamiltonian. In this paper we investigate a further condition and prove that if G is a connected graph of order n і 3 such that d(G) і (n-2)/2, then G is Hamiltonian or G belongs to four classes of well-structured exceptional graphs.
Wong, Pak-Ken (1997)
International Journal of Mathematics and Mathematical Sciences
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Z. Skupień (1989)
Banach Center Publications
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Ronald J. Gould (1981)
Colloquium Mathematicae
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Jill R. Faudree, Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson, Colton Magnant (2010)
Discussiones Mathematicae Graph Theory
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The Chvátal-Erdös theorems imply that if G is a graph of order n ≥ 3 with κ(G) ≥ α(G), then G is hamiltonian, and if κ(G) > α(G), then G is hamiltonian-connected. We generalize these results by replacing the connectivity and independence number conditions with a weaker minimum degree and independence number condition in the presence of sufficient connectivity. More specifically, it is noted that if G is a graph of order n and k ≥ 2 is a positive integer such that κ(G) ≥ k, δ(G) >...
Tudor Zamfirescu (1971)
Rendiconti del Seminario Matematico della Università di Padova
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Magdalena Bojarska (2010)
Discussiones Mathematicae Graph Theory
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We show that every 2-connected (2)-Halin graph is Hamiltonian.
Erhard Hexel (2017)
Discussiones Mathematicae Graph Theory
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The H-force number h(G) of a hamiltonian graph G is the smallest cardinality of a set A ⊆ V (G) such that each cycle containing all vertices of A is hamiltonian. In this paper a lower and an upper bound of h(G) is given. Such graphs, for which h(G) assumes the lower bound are characterized by a cycle extendability property. The H-force number of hamiltonian graphs which are exactly 2-connected can be calculated by a decomposition formula.
Yong Lu, Qiannan Zhou (2022)
Czechoslovak Mathematical Journal
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During the last decade, several research groups have published results on sufficient conditions for the hamiltonicity of graphs by using some topological indices. We mainly study hyper-Zagreb index and some hamiltonian properties. We give some sufficient conditions for graphs to be traceable, hamiltonian or Hamilton-connected in terms of their hyper-Zagreb indices. In addition, we also use the hyper-Zagreb index of the complement of a graph to present a sufficient condition for it to...
Boris Khesin (1993)
Recherche Coopérative sur Programme n°25
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E. Zenhder (1975)
Publications mathématiques et informatique de Rennes
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Demovič, A. (1995)
Acta Mathematica Universitatis Comenianae. New Series
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Moshe Rosenfeld (1989)
Aequationes mathematicae
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Jianxiang Cao, Minyong Shi, Lihua Feng (2016)
Discussiones Mathematicae Graph Theory
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The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network Qn, and has been proved to have better properties than Qn with the same number of links and processors. For a bipartite graph G = (V0 ∪ V1,E), we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v ∈ Vi, i ∈ {0, 1}, any edge e ∈ E(G − v), there is a Hamiltonian path containing e in G − v between any two vertices of V1−i. In this paper, we prove that BHn...