Continuous forcing spectra of perfect matchings of convex hexagonal systems

A convex hexagonal system is a hexagonal system whose inner dual graph has the convex polygonal boundary. A forcing set S for a perfect matching M of a graph G is a subset of M that is contained in no other perfect matchings of G. The smallest cardinality of a forcing set of M is called the forcing number of M, denoted by f(G, M). The forcing spectrum of G is defined as: Spec(G) = {f(G, M)|M is a perfect matching of G}. In this paper, we show that for any convex hexagonal system O(m, k, n) with a perfect matching, its forcing spectrum is continuous i.e. an integer interval.