Five-Connected Toroidal Graphs Are Hamiltonian

@article{Thomas1997FiveConnectedTG,
  title={Five-Connected Toroidal Graphs Are Hamiltonian},
  author={Robin Thomas and Xingxing Yu},
  journal={J. Comb. Theory, Ser. B},
  year={1997},
  volume={69},
  pages={79-96}
}
We prove that every edge in a 5-connected graph embedded in the torus is contained in a Hamilton cycle. Our proof is constructive and implies a polynomial time algorithm for finding a Hamilton cycle. 

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5-Connected Toroidal Graphs are Hamiltonian-Connected

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