For　positive　integers　k　＞=　2　and　m,　let　g(k)　(m)　be　the　smallest　integer　such　that　for　each　graph　G　with　m　edges　there　exists　a　k-partition　V　(G)　=　V-1　boolean　OR　.　.　.　boolean　OR　V-k　in　which　each　V-i　contains　at　most　g(k)　(m)　edges.　Bollobas　and　Scott　showed　that　g(k)　(m)　＜=　m/k(2)　+　k-1/2k(2)　(root　2m　+　root　1/4　-　1/2).　Ma　and　Yu　posed　the　following　problem:　is　it　true　that　the　limsup　of　m/k(2)　+　k-1/2k(2)　root　2m　-　g(k)　(m)　tends　to　infinity　asmtends　to　infinity?　They　showed　it　holds　when　k　is　even,　establishing　a　conjecture　of　Bollobas　and　Scott.　In　this　article,　we　solve　the　problem　completely.　We　also　present　a　result　by　showing　that　every　graph　with　a　large　k-cut　has　a　k-partition　in　which　each　vertex　class　contains　relatively　few　edges,　which　partly　improves　a　result　given　by　Bollobas　and　Scott.　(C)　2016　Wiley　Periodicals,　Inc.