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Optimal bisections of directed graphs

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arxiv 2302.04050 v1 pith:VREBRIV7 submitted 2023-02-08 math.CO

Guanwu Liu , Jie Ma , Chunlei Zu This is my paper · ORCID
classification math.CO
keywords directedarcsbisectionsgraphsleastoptimaladmitsanswer
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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.

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