Complete-Subgraph-Transversal-Sets problem on bounded treewidth graphs

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.