论文标题
完全强迫六边形系统的数量
The complete forcing numbers of hexagonal systems
论文作者
论文摘要
令G为具有完美匹配的图形。 G的完整强迫集是G的一个子集，每个完美匹配的限制是其强迫集。 G的完整强迫数是G。Xu等人的完整强迫集的最小基数。给出了一个完整的强迫集的表征，并为完整的CATA符合的六角形系统提供了一些明确的公式。在本文中，我们考虑一般的六边形系统。我们在基本边缘切割盖和两个下限的六角形系统的完整强迫数量上呈现了上限，分别通过六角形数量和匹配数。作为应用，我们获得了一些明确的公式，用于完全强迫某些类型的六角形系统，包括平行四边形，常规六边形和矩形形状的六边形系统。
Let G be a graph with a perfect matching. A complete forcing set of G is a subset of edges of G to which the restriction of every perfect matching is a forcing set of it. The complete forcing number of G is the minimum cardinality of complete forcing sets of G. Xu et al. gave a characterization for a complete forcing set and derived some explicit formulas for the complete forcing numbers of cata-condensed hexagonal systems. In this paper, we consider general hexagonal systems. We present an upper bound on the complete forcing numbers of hexagonal systems in terms of elementary edge-cut cover and two lower bounds by the number of hexagons and matching number respectively. As applications, we obtain some explicit formulas for the complete forcing numbers of some types of hexagonal systems including parallelogram, regular hexagon- and rectangle-shaped hexagonal systems.
