Regularity of powers of cover ideals of bipartite graphs

Let [Formula: see text] be a bipartite graph over the vertex set [Formula: see text] and let [Formula: see text] be the cover ideal of [Formula: see text] in the polynomial ring [Formula: see text]. It is known that there are integers [Formula: see text] and [Formula: see text] such that [Formula: see text] is a linear function in [Formula: see text] for all [Formula: see text]. In this paper, we give effective bounds for [Formula: see text] and [Formula: see text].