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-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P 6 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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Supported by NSFC (Grant No. 11271300); the Natural Science Foundation of Shaanxi Province (Grant No. 2016JQ1002), and the Project NEXLIZ–CZ.1.07/2.3.00/30.0038
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Li, B.L., Ning, B. & Zhang, S.G. Degree conditions restricted to induced paths for hamiltonicity of claw-heavy graphs. Acta. Math. Sin.-English Ser. 33, 301–310 (2017). https://doi.org/10.1007/s10114-016-5735-5
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DOI: https://doi.org/10.1007/s10114-016-5735-5