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arXiv · 1506.05540

Degree conditions restricted to induced paths for hamiltonicity of claw-heavy graphs

Binlong Li·Bo Ning·Shenggui Zhang
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Abstract

Broersma and Veldman proved that every 2-connected claw-free and $P_6$-free graph is hamiltonian. Chen et al. extended this result by proving every 2-connected claw-heavy and $P_6$-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and $P_6$-\emph{o}-heavy but not hamiltonian. In this paper we further give some Ore-type degree conditions restricting to induced $P_6$'s of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.

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Binlong Li, Bo Ning, Shenggui Zhang. 2015-06-18. Degree conditions restricted to induced paths for hamiltonicity of claw-heavy graphs. https://doi.org/10.1007/s10114-016-5735-5

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