Vertices of Small Degree in Uniquely Hamiltonian Graphs

Vertices of Small Degree in Uniquely Hamiltonian Graphs

LetGbe a uniquely hamiltonian graph onnvertices. We show thatGhas a vertex of degree at mostclog28n+3, wherec=(2−log23)−1≈2.41. We show further thatGhas at least two vertices of degree less than four if it is planar and at least four vertices of degree two if it is bipartite.

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Veröffentlicht in:Journal of combinatorial theory. Series B 1998-11, Vol.74 (2), p.265-275
Hauptverfasser: Bondy, J.A., Jackson, Bill
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container_title Journal of combinatorial theory. Series B
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Jackson, Bill
description LetGbe a uniquely hamiltonian graph onnvertices. We show thatGhas a vertex of degree at mostclog28n+3, wherec=(2−log23)−1≈2.41. We show further thatGhas at least two vertices of degree less than four if it is planar and at least four vertices of degree two if it is bipartite.
doi_str_mv 10.1006/jctb.1998.1845
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title Vertices of Small Degree in Uniquely Hamiltonian Graphs
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