Abstract
In this paper we address the problem of finding an induced interval graph with a maximum number of vertices in a given graph G. We show that the problem is NP-complete for bipartite planar graphs and split graphs. We can show that there exist efficient algorithms for graphs with bounded treewidth, (tree=)cographs, and distance heredlitary graphs. We show that there exists an efficient algorithm for graphs which are intersection graphs of intervals on lines intersecting in one point.