The competition number of a graph with exactly image holes, all of which are independent Original Research Article

Given an acyclic digraph image, the competition graph image of image is the graph with the same vertex set as image where two distinct vertices image and image are adjacent in image if and only if there is a vertex image in image such that image and image are arcs of image. The competition number image of a graph image is the least number of isolated vertices that must be added to image to form a competition graph. The purpose of this paper is to prove that the competition number of a graph with exactly image holes, all of which are independent, is at most image. This generalizes the result for image given by Roberts, and the result for image given by Cho and Kim.