  Given a bipartite graph with bipartition $(A,B)$ where $B$ is equipartitioned
into $k\ge2$ blocks, can the vertices in $A$ be picked one by one so that at
every step, the picked vertices cover roughly the same number of vertices in
each of these blocks? We show that, if each block has cardinality $m$ say, the
vertices in $B$ have the same degree, and each vertex in $A$ has at most $cm$
neighbors in every block where $c>0$ is a small constant, then there is an
ordering $v_1,\ldots,v_n$ of the vertices in $A$ such that for every
$j\in\{1,\ldots,n\}$, the numbers of vertices with a neighbor in
$\{v_1,\ldots,v_j\}$ in every two blocks differ by at most
$\sqrt{2(k-1)}c^{1/2}m$. This is related to a well-known lemma of Steinitz, and
partially answers an unpublished question of Scott and Seymour.
