Optimal bisections of directed graphs

Guanwu Liu; Jie Ma; Chunlei Zu

Optimal bisections of directed graphs

Combinatorics 2023-02-09 v1

Authors: Guanwu Liu , Jie Ma , Chunlei Zu

Abstract

In this paper, motivated by a problem of Scott and a conjecture of Lee, Loh and Sudakov we consider bisections of directed graphs. We prove that every directed graph with $m$ arcs and minimum semidegree at least $d$ admits a bisection in which at least $\left(\frac{d}{2(2d+1)}+o(1)\right)m$ arcs cross in each direction. This provides an optimal bound as well as a positive answer to a question of Hou and Wu in a stronger form.

Keywords

graph theory bipartite graphs graph pebbling

Cite

@article{arxiv.2302.04050,
  title  = {Optimal bisections of directed graphs},
  author = {Guanwu Liu and Jie Ma and Chunlei Zu},
  journal= {arXiv preprint arXiv:2302.04050},
  year   = {2023}
}

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