Judicious　partitioning　problems　on　graphs　ask　for　partitions　that　bound　several　quantities　simultaneously,　which　have　received　much　attention　lately.　Scott　(2005)　asked　the　following　natural　question:　What　is　the　maximum　constant　c(d)　such　that　every　directed　graph　D　with　m　arcs　and　minimum　outdegree　d　admits　a　bipartition　V(D)　=　V-1　?　V-2　satisfying　min{e(V-1,　V-2),　e(V-2,　V1)}　＞　c(d)m?　Here,　for　i　=　1,　2,　e(V-i,　V3-i)　denotes　the　number　of　arcs　in　D　from　V-i　to　V3-i.　Lee　et　al.　(2016)　conjectured　that　every　directed　graph　D　with　m　arcs　and　minimum　outdegree　at　least　d　＞　2　admits　a　bipartition　V(D)　=　V-1　?　V-2　such　that　minfe(V-1;　V-2);　e(V-2;　V-1)g　＞　(d　1　-　2(2d　1)　+　o(1))　m:　In　this　paper,　we　show　that　this　conjecture　holds　under　the　additional　natural　condition　that　the　minimum　indegree　is　also　at　least　d.