A generalization of Bondy's and Fan's sufficient conditions for Hamiltonian graphs

@article{Liu1997AGO,
  title={A generalization of Bondy's and Fan's sufficient conditions for Hamiltonian graphs},
  author={Xin Liu and Bo Wei},
  journal={Discrete Mathematics},
  year={1997},
  volume={169},
  pages={249-255}
}
Let G be a k-connected (k ~> 2) graph on n vertices. Let S be an independent set of G. S is called essential if there exists two distinct vertices in S which have a common neighbor in G. In this paper we shall prove that ifmax{d(u): u ~ S} >~ n/2 holds for any essential independent set S with k + 1 vertices of G, then either G is hamiltonian or G is one of three classes of exceptional graphs. This is motivated by a result of Chen et al. (1994) and generalizes the results of Bondy (1980) and Fan… CONTINUE READING

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