## Displaying similar documents to “Bridges and Hamiltonian circuits in planar graphs.”

### On n-distant Hamiltonian line graphs.

Aequationes mathematicae

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### Hamiltonian Lines in Infinite Graphs with Few Verticles of Small Valency

Aequationes mathematicae

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### Pairs of edge disjoint Hamiltonian circuits in 5-connected planar graphs.

Aequationes mathematicae

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### Pairs of edge-disjoint Hamiltonian circuits.

Aequationes mathematicae

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### On Hamiltonian properties of powers of special Hamiltonian graphs

Colloquium Mathematicae

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### New sufficient conditions for hamiltonian and pancyclic graphs

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

Discussiones Mathematicae Graph Theory

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### A note on Hamiltonian cycles in generalized Halin graphs

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

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

Fundamenta Mathematicae

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### On n-distant Hamiltonian line graphs. (Short Communication).

Aequationes mathematicae

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### On Uniquely Hamiltonian Claw-Free and Triangle-Free Graphs

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. ...

### Edge-disjoint Hamilton cycles in 4-regular planar graphs.

Aequationes mathematicae

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