Zhaoyang Ma

Sharp Bisection Bounds for Digraphs

Fix an integer $d\ge1$. We prove that, for all sufficiently large $m$, every digraph $D$ with $m$ arcs and minimum semidegree at least $d$ admits a bisection $V(D)=V_1\cup V_2$ with $\bigl||V_1|-|V_2|\bigr|\le1$ such that \[ \min\{e(V_1,V_2),e(V_2,V_1)\} \ge \frac{d(m+d+1)}{2(2d+1)}. \] Here, for disjoint vertex sets $...