Vertices of Small Degree in Uniquely Hamiltonian Graphs

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Abstract

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. © 1998 Academic Press.

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Bondy, J. A., & Jackson, B. (1998). Vertices of Small Degree in Uniquely Hamiltonian Graphs. Journal of Combinatorial Theory. Series B, 74(2), 265–275. https://doi.org/10.1006/jctb.1998.1845

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