In this paper we propose an algorithm for generating maximum weight independent sets in a circle graph, that is, for putting out all maximum weight independent sets one by one without duplication. The time complexity is O(n3 + β ), where n is the number of vertices, β output size, i. e. , the sum of the cardinalities of the output sets. It is shown that the same approach can be applied for spider graphs and for circular-arc overlap graphs.

Let G = (A, B, E) be a bipartite graph with bipartition (A:B) of vertex set and edge set E. For each vertex v, Γ(v) denotes the set of adjacent vertices to v. G is said to be t-convex on the vertex set A if there is a tree and a one-to-one correspondence between vertices in A and edges of the tree such that for each vertex b B the edges of the tree corresponding to vertices in Γ(b) form a path on the tree. G is doubly t-convex if it is convex both on vertex set A and on B. In this paper, we show that, the class of doubly t-convex graphs is exactly the class of bipartite circle graphs.