Computing the Clique-width of Cactus Graphs

Similar to the tree-width (twd), the clique-width (cwd) is an invariant of graphs. A well known relationship between tree-width and clique-width is that cwd(G)≤3⋅2twd(G)−1. It is also known that tree-width of Cactus graphs is 2, therefore the clique-width for those graphs is smaller or equal than 6. In this paper, it is shown that the clique-width of Cactus graphs is smaller or equal to 4 and we present a polynomial time algorithm which computes exactly a 4-expression.