Approximating Longest Cycles in Graphs with Bounded Degrees

@article{Chen2006ApproximatingLC,
  title={Approximating Longest Cycles in Graphs with Bounded Degrees},
  author={Guantao Chen and Zhicheng Gao and Xingxing Yu and Wenan Zang},
  journal={SIAM J. Comput.},
  year={2006},
  volume={36},
  pages={635-656}
}
Jackson and Wormald conjectured that if G is a 3-connected n-vertex graph with maximum degree d ≥ 4 then G has a cycle of length Ω(nd−1 ) and showed that the bound is best possible if true. In this paper we prove that this conjecture holds when d− 1 is replaced by max{64, 4d + 1}. Our proof implies a cubic algorithm for finding such a cycle. 

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