On n-distant Hamiltonian line graphs.
Linda M. Lesniak (1978)
Aequationes mathematicae
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Displaying similar documents to “Bridges and Hamiltonian circuits in planar graphs.”
On n-distant Hamiltonian line graphs.
Hamiltonian Lines in Infinite Graphs with Few Verticles of Small Valency
C.ST.J.A. NASH-WILLIAMS (1971)
Aequationes mathematicae
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Pairs of edge disjoint Hamiltonian circuits in 5-connected planar graphs.
Moshe Rosenfeld (1989)
Aequationes mathematicae
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Pairs of edge-disjoint Hamiltonian circuits.
Branko Grünbaum, J. Malkevitch (1976)
Aequationes mathematicae
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On Hamiltonian properties of powers of special Hamiltonian graphs
Gary Chartrand, S. F. Kapoor (1974)
Colloquium Mathematicae
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New sufficient conditions for hamiltonian and pancyclic graphs
Ingo Schiermeyer, Mariusz Woźniak (2007)
Discussiones Mathematicae Graph Theory
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For a graph G of order n we consider the unique partition of its vertex set V(G) = A ∪ B with A = {v ∈ V(G): d(v) ≥ n/2} and B = {v ∈ V(G):d(v) < n/2}. Imposing conditions on the vertices of the set B we obtain new sufficient conditions for hamiltonian and pancyclic graphs.
Trestles in polyhedral graphs
Michal Tkáč, Heinz-Jürgen Voss (2002)
Discussiones Mathematicae Graph Theory
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A note on Hamiltonian cycles in generalized Halin graphs
Magdalena Bojarska (2010)
Discussiones Mathematicae Graph Theory
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We show that every 2-connected (2)-Halin graph is Hamiltonian.
A note on the Song-Zhang theorem for Hamiltonian graphs
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...
Locally Hamiltonian and planar graphs
Zdzisław Skupień (1966)
Fundamenta Mathematicae
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On n-distant Hamiltonian line graphs. (Short Communication).
Linda M. Lesniak (1977)
Aequationes mathematicae
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On Uniquely Hamiltonian Claw-Free and Triangle-Free Graphs
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. ...
On hyper-Zagreb index conditions for hamiltonicity of graphs
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...