Let　G　be　a　weighted　hypergraph　with　edges　of　size　at　most　2.　Bollobás　and　Scott　conjectured　that　G　admits　a　bipartition　such　that　each　vertex　class　meets　edges　of　total　weight　at　least　(w1−Δ1)/2+2w2/3,　where　wi　is　the　total　weight　of　edges　of　size　i　and　Δ1　is　the　maximum　weight　of　an　edge　of　size　1.　In　this　paper,　for　positive　integer　weighted　hypergraph　G　(i.e.,　multi-hypergraph),　we　show　that　there　exists　a　bipartition　of　G　such　that　each　vertex　class　meets　edges　of　total　weight　at　least　(w0−1)/6+(w1−Δ1)/3+2w2/3,　where　w0　is　the　number　of　edges　of　size　1.　This　generalizes　a　result　of　Haslegrave.　Based　on　this　result,　we　show　that　every　graph　with　m　edges,　except　for　K2　and　K1,3,　admits　a　tripartition　such　that　each　vertex　class　meets　at　least　[2m/5]　edges,　which　establishes　a　special　case　of　a　more　general　conjecture　of　Bollobás　and　Scott.　©　2017,　Institute　of　Mathematics　of　the　Academy　of　Sciences　of　the　Czech　Republic,　Praha,　Czech　Republic.