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 B. Wei},
  journal={Discret. Math.},
  year={1997},
  volume={169},
  pages={249-255}
}
  • Xin Liu, B. Wei
  • Published 1997
  • Mathematics, Computer Science
  • Discret. Math.
  • Abstract 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 if max { 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… CONTINUE READING

    Topics from this paper.

    A note on the SongZhang theorem for Hamiltonian graphs
    • 3
    • Highly Influenced
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-7 OF 7 REFERENCES
    New sufficient conditions for cycles in graphs
    • G. Fan
    • Mathematics, Computer Science
    • 1984
    • 169
    A note on Hamiltonian circuits
    • 510
    • PDF
    Erd6s, A note on hamiltonian circuits
    • 1972
    Essential independent set and hamiltonian cycles, J.G.T
    • 1996
    Graph Theory with Applications
    • 6,429
    • PDF
    Longest paths and cycles in graphs of high degree, Research Report CORR80-16
    • 1980