Trestles in polyhedral graphs
Michal Tkáč, Heinz-Jürgen Voss (2002)
Discussiones Mathematicae Graph Theory
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Michal Tkáč, Heinz-Jürgen Voss (2002)
Discussiones Mathematicae Graph Theory
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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...
Bohdan Zelinka (1998)
Discussiones Mathematicae Graph Theory
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Two classes of graphs which are maximal with respect to the absence of Hamiltonian paths are presented. Block graphs with this property are characterized.
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...
Z. Skupień (1974)
Colloquium Mathematicae
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Ben Seamone (2015)
Discussiones Mathematicae Graph Theory
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A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. In this note, we prove that claw-free graphs with minimum degree at least 3 are not uniquely Hamiltonian. We also show that this is best possible by exhibiting uniquely Hamiltonian claw-free graphs with minimum degree 2 and arbitrary maximum degree. Finally, we show that a construction due to Entringer and Swart can be modified to construct triangle-free uniquely Hamiltonian graphs with minimum degree 3. ...
Gary Chartrand, S. F. Kapoor (1974)
Colloquium Mathematicae
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Linda M. Lesniak (1978)
Aequationes mathematicae
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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.
Ngo Dac Tan, Le Xuan Hung (2004)
Discussiones Mathematicae Graph Theory
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A graph G is called a split graph if the vertex-set V of G can be partitioned into two subsets V₁ and V₂ such that the subgraphs of G induced by V₁ and V₂ are empty and complete, respectively. In this paper, we characterize hamiltonian graphs in the class of split graphs with minimum degree δ at least |V₁| - 2.
Ronald J. Gould (1981)
Colloquium Mathematicae
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Jerzy A. Filar, Michael Haythorpe, Giang T. Nguyen (2010)
Discussiones Mathematicae Graph Theory
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Almost all d-regular graphs are Hamiltonian, for d ≥ 3 [8]. In this note we conjecture that in a similar, yet somewhat different, sense almost all cubic non-Hamiltonian graphs are bridge graphs, and present supporting empirical results for this prevalence of the latter among all connected cubic non-Hamiltonian graphs.
Bullock, Frank, Frick, Marietjie, Singleton, Joy, van Aardt, Susan, Mynhardt, Kieka (C.M.) (2008)
The Electronic Journal of Combinatorics [electronic only]
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(1975)
Czechoslovak Mathematical Journal
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