Complete forcing numbers of primitive coronoids

Let G be a graph with edge set E(G) that admits a perfect matching M. A forcing set of M is a subset of M contained in no other perfect matching of G. A complete forcing set of G, recently introduced by Xu et al. (J Combin Optim 29(4):803–814, 2015c), is a subset of E(G) to which the restriction of any perfect matching is a forcing set of the perfect matching. The minimum possible cardinality of a complete forcing set of G is the complete forcing number of G. Previously, Xu et al. (J Combin Optim 29(4):803–814, 2015c) gave an expression for the complete forcing number of a hexagonal chain and a recurrence relation for complete forcing numbers of catacondensed hexagonal systems. In this article, by the constructive proof, we give an explicit analytical expression for the complete forcing number of a primitive coronoid, a circular single chain consisting of congruent regular hexagons (i.e., Theorem 3.9). Copyright © 2015 Springer Science+Business Media New York.