An on-line vertex coloring algorithm receives vertices of a graph in some externally determined order. Each new vertex is presented together with a set of the edges connecting it to the previously presented vertices. As a vertex is presented, the algorithm assigns it a color which cannot be changed afterwards. The on-line coloring problem was addressed for many different classes of graphs defined in terms of forbidden structures. We analyze the class of Is-free graphs, i.e., graphs in which the maximal size of an independent set is at most s-1. An old Szemerédi's result implies that for each on-line algorithm A there exists an on-line presentation of an Is-free graph G forcing A to use at least s / 2χ(G) colors. We prove that any greedy algorithm uses at most s / 2χ(G) colors for any on-line presentation of any Is-free graph G. Since the class of co-planar graphs is a subclass of I5-free graphs all greedy algorithms use at most 5 / 2χ(G) colors for co-planar G's. We prove that, even in a smaller class, this is an almost tight bound.