Jiang found a polynomial-time algorithm for solving what he calls "labelled multistage graphs" Note that these graphs are partially ordered sets (http://en.wik

Jiang found a polynomial-time algorithm for solving what he calls "labelled multistage graphs" Note that these graphs are partially ordered sets (http://en.wikipedia.org/wiki/Partially_ordered_set http://en.wikipedia.org/wiki/Partially_ordered_set) and every partially ordered set has a unique corresponding comparability graph (http://en.wikipedia.org/wiki/Comparability_graph http://en.wikipedia.org/wiki/Comparability_graph) and the problem of finding a Hamiltonian cycle in a comparability graph is known not to be NP-complete. (http://link.springer.com/article/10.1007%2FBF00571188 http://link.springer.com/article/10.1007%2FBF00571188) Thus Jiang may have found a polynomial-time algorithm, but it solves a problem that is not NP-complete.