A complete forcing set of a graph G with a perfect matching is a subset of E(G) on which the restriction of each perfect matching M is a forcing set of M. The complete forcing number of G is the minimum cardinality of complete forcing sets of G. It was shown that a complete forcing set of G also antiforces each perfect matching. Previously, some closed formulas for the complete forcing numbers of some types of hexagonal systems including cata-condensed hexagonal systems and parallelograms have been derived. In this paper, we show that the subset of E(G) obtained from E(G) by deleting all edges that are incident with some vertices of a 2-independent set of G is a complete forcing set. As applications, we give some expressions for the complete forcing numbers of complete multipartite graphs, 2n-vertex graphs with minimum degree at least \(2n-3\) and 2n-vertex balanced bipartite graphs with minimum degree at least \(n-2\), by showing that each sufficiently short cycle is a nice cycle.

具有完美匹配的图G的完全强迫集是E ( G )的子集，其中每个完美匹配M的限制是M的强迫集。G的完全强迫数是G的完全强迫集的最小基数。结果表明，G的完整强迫集也反力每个完美匹配。此前，已经导出了一些六角形系统（包括压缩六角形系统和平行四边形）的完全受力数的封闭公式。在本文中，我们证明了E ( G ) 的子集由通过删除与G的 2 个独立集的某些顶点相关的所有边，E ( G )是一个完全力集。作为应用，我们给出了完全多分图、最小度至少为\(2n-3\)的 2 n顶点图和最小度至少为\(n的2 n顶点平衡二部图的完全强迫数的表达式。-2\)，通过表明每个足够短的周期都是一个很好的周期。