Let \(G=(V,E)\) be a graph. A complete subgraph of G is a subgraph of pairwise adjacent vertices of V of size at least 2. Let \(\Phi _C(G)\) be the set of all complete subgraphs of G and \(\Phi \subseteq {\Phi }_C(G)\). In this paper, we consider the Complete-Subgraph-Transversal-Set on \(\Phi \) problem and the L-Max Complete-Subgraph-Transversal-Set on \(\Phi \) problem. We give polynomial time algorithms to these two problems on graphs of bounded treewidth. At last, we show the connections between these two problems with some other NP-complete problems, for example Clique-Transversal-Set problem on graphs and Vertex-Cover problem on hypergraphs.

令\（G =（V，E）\）为图。G的完整子图是大小至少为2的V的成对相邻顶点的子图。令\（\ Phi _C（G）\）是G和\（\ Phi \ subseteq {\ Phi } _C（G）\）。在本文中，我们考虑了完整的-子图的横置设置上\（\披\）问题和大号-最大的Complete-子图的横置设置上\（\披\）问题。我们对有界树宽图上的这两个问题给出多项式时间算法。最后，我们展示了这两个问题与其他一些NP完全问题之间的联系，例如图上的Clique-Transversal-Set问题和超图上的Vertex-Cover问题。