Affiliation:
1. School of Mathematics and Statistics Shandong University of Technology Zibo Shandong China
2. School of Mathematical Sciences University of Science and Technology of China Hefei Anhui China
3. Hefei National Laboratory University of Science and Technology of China Hefei Anhui China
4. School of Mathematical Sciences Shanghai Jiao Tong University Shanghai China
Abstract
AbstractIn this article, motivated by a problem of Scott [Surveys in combinatorics, 327 (2005), 95‐117.] and a conjecture of Lee et al. [Random Struct. Algorithm, 48 (2016), 147‐170.] we consider bisections of directed graphs. We prove that every directed graph with arcs and minimum semidegree at least admits a bisection in which at least arcs cross in each direction. This provides an optimal bound as well as a positive answer to a question of Hou and Wu [J. Comb. Theory B, 132 (2018), 107‐133.] in a stronger form.
Funder
National Key Research and Development Program of China
National Natural Science Foundation of China
China Postdoctoral Science Foundation
Subject
Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software