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On Uniquely Hamiltonian Claw-Free and Triangle-Free Graphs

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Seamone B.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 2

207-214

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.

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1 Discussiones Mathematicae Graph Theory

1 Seamone B.

1 2015

Wyniki wyszukiwania

On Uniquely Hamiltonian Claw-Free and Triangle-Free Graphs