Bollobàs and Scott conjectured that every graph $G$ has a balanced bipartite spanning subgraph $H$ such that for each $v\\in V(G)$ , $d_H(v)\\ge (d_G(v)-1)/2$. In this talk, we show that every graphic sequence has a realization for which this Bollobàs-Scott conjecture holds, confirming a conjecture of Hartke and Seacrest. On the other hand, we use an infinite family of graphs to illustrate that $\\lfloor (d_G(v)-1)/2 \floor$ (rather than $(d_G(v)-1)/2$ ) may have been the intended lower bound by Bollobàs and Scott.