@article{Nishiyama2018ThePH,
title={The parity Hamiltonian cycle problem},
author={H. Nishiyama and Y. Kobayashi and Y. Yamauchi and Shuji Kijima and M. Yamashita},
journal={Discret. Math.},
year={2018},
volume={341},
pages={606-626}
}

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