Given a graph G, a subgraph C is called a clique of G if C is a complete subgraph of G maximal under inclusion and ｜C｜ ≥2. A clique-transversal set S of G is a set of vertices of G such that S meets all cliques of ...Given a graph G, a subgraph C is called a clique of G if C is a complete subgraph of G maximal under inclusion and ｜C｜ ≥2. A clique-transversal set S of G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted as τC（G）, is the minimum cardinality of a clique-transversal set in G. The clique-graph of G, denoted as K（G）, is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques in G have nonempty intersection. Let F be a class of graphs G such that F = {G｜ K（G） is a tree}. In this paper the graphs in F having independent clique-transversal sets are shown and thus τC（G）/｜G｜ ≤ 1/2 for all G ∈F.展开更多
基金supported by the foundation from Department of Education of Zhejiang Province (No.Y201018696)the Nature Science Foundation of Anhui Provincial Education Department(No. KJ2011B090)
基金Project supported by the National Natural Science Foundation of China （Grant No.10571117）, and the Development Foundation of Shanghai Municipal Commission of Education （Grant No.05AZ04）
文摘Given a graph G, a subgraph C is called a clique of G if C is a complete subgraph of G maximal under inclusion and ｜C｜ ≥2. A clique-transversal set S of G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted as τC（G）, is the minimum cardinality of a clique-transversal set in G. The clique-graph of G, denoted as K（G）, is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques in G have nonempty intersection. Let F be a class of graphs G such that F = {G｜ K（G） is a tree}. In this paper the graphs in F having independent clique-transversal sets are shown and thus τC（G）/｜G｜ ≤ 1/2 for all G ∈F.
