Five-Connected Toroidal Graphs Are Hamiltonian

  title={Five-Connected Toroidal Graphs Are Hamiltonian},
  author={Robin Thomas and Xingxing Yu},
  journal={J. Comb. Theory, Ser. B},
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. Published in J. Combin. Theory Ser. B 69 (1997), no. 1, 79–96. partially supported by NSF grants DMS-9103480 and DMS-9303761 partially supported by NSF grants DMS-9105173 and DMS-9301909