Generalized hexagonal systems with each hexagon being resonant

AbstractAn edge of a generalized hexagonal system H is said to be not fixed if it belongs to some but not all perfect matchings of H. In this paper we give a necessary and sufficient condition for a generalized hexagonal system in which every edge is not fixed. Applying the above result to complete generalized hexagonal systems, we obtain a simple criterion to determine whether or not each hexagon of a complete generalized hexagonal system is resonant, and give a new and simpler proof of the main theorem of [4]