Hamiltonian Cycles in Permutation Graphs

In this paper, we employ the structures of a permutation graph as exhibited in the Euclidean representation to solve the existence and construction problems of Hamiltonian cycles on permutation graphs. We define and prove the existence of a layered Hamiltonian cycle in a Hamiltonian permutation graph. A linear (in size) time and (in order) space algorithm for construction of a layered Hamiltonian cycle on a permutation graph is presented and its
correctness proven.