For　positive　integers　k　≥　2　and　m,　let　gk(m)　be　the　smallest　integer　such　that　for　each　graph　G　with　m　edges　there　exists　a　k-partition　V(G)=　V1　U...UVk　in　which　each　Vi　contains　at　most　gk　(m)　edges.　Bollobás　and　Scott　showed　that　gk(m)≤　m/k2　+k-1/2k2　(√2m+1/4　-1/2).　Ma　and　Yu　posed　the　following　problem:　is　it　true　that　the　limsup　of　m\k2+k-1\2k2√2m　-gk(m)　tends　to　infinity　as　m　tends　to　infinity?　They　showed　it　holds　when　k　is　even,　establishing　a　conjecture　of　Bollobás　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　Bollobás　and　Scott.　©　2016　Wiley　Periodicals,　Inc.