The parity Hamiltonian cycle problem

  title={The parity Hamiltonian cycle problem},
  author={H. Nishiyama and Y. Kobayashi and Y. Yamauchi and Shuji Kijima and M. Yamashita},
  journal={Discret. Math.},
  • H. Nishiyama, Y. Kobayashi, +2 authors M. Yamashita
  • Published 2018
  • Mathematics, Computer Science
  • Discret. Math.
  • Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a closed walk which visits every vertex an odd number of times, where we remark that the walk may use an edge more than once. First, we give a complete characterization of the graphs which have PHCs, and give a linear time algorithm to find a PHC, in which every edge appears at most four times, in fact. In contrast, we show that finding a… CONTINUE READING

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