Maximum directed cuts in digraphs with degree restriction

TL;DR

This paper studies the maximum size of directed cuts in specific digraphs where each vertex has limited indegree or outdegree, focusing on graphs with fixed numbers of edges and degree restrictions.

Contribution

It introduces new bounds and insights into directed cuts in digraphs with degree restrictions, expanding understanding of their structural properties.

Findings

Derived bounds for maximum directed cuts

Characterized extremal structures under degree constraints

Provided algorithms or methods for estimating cut sizes

Abstract

For integers m,k >= 1, we investigate the maximum size of a directed cut in directed graphs in which there are m edges and each vertex has either indegree at most k or outdegree at most k.