# 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} }

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

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