Rooted minor problems in highly connected graphs

he purpose of this note is to give a connectivity condition for a graph to have a rooted complete bipartite minor. Here, a rooted complete bipartite graph minor image means that for any distinct k vertices image, there are connected subgraphs image such that each of image contains image and is adjacent to all image. Roughly, our results say that if G is large enough, then the linear connectivity on the function of k guarantees the existence of a rooted image-minor (for any a), and in general, the connectivity condition on the existence of a rooted image-minor is “almost” the same as the average degree which forces the existence of a image-minor.