A　bisection　of　a　graph　is　a　bipartition　of　its　vertex　set　in　which　the　number　of　vertices　in　the　two　parts　differ　by　at　most　1,　and　its　size　is　the　number　of　edges　which　go　across　the　two　parts.　Let　(Formula　presented.)　be　a　graph　with　(Formula　presented.)　vertices　and　(Formula　presented.)　edges.　Bollobás　and　Scott　asked　the　following:　What　are　the　largest　and　smallest　cuts　that　we　can　guarantee　with　bisections　of　(Formula　presented.)　?　There　are　reasonable　sufficient　conditions　such　that　(Formula　presented.)　has　bisections　of　size　at　least　(Formula　presented.)　for　some　(Formula　presented.).　In　this　paper,　we　study　the　Min-Bisection　problem　which　has　arisen　in　numerous　contexts,　and　initially　give　some　sufficient　conditions　such　that　(Formula　presented.)　has　bisections　of　size　at　most　(Formula　presented.)　for　some　(Formula　presented.).　©　2025　Wiley　Periodicals　LLC.