Packing directed circuits exactly

TL;DR

This paper characterizes digraphs where the maximum number of disjoint circuits equals the minimum feedback vertex set size in every subdigraph, providing structural insights into such graphs.

Contribution

It offers an excluded minor and structural characterization of digraphs with this circuit packing property, advancing understanding of digraph circuit packings.

Findings

Provides an excluded minor characterization.

Establishes a structural description of these digraphs.

Enhances understanding of circuit packing in directed graphs.

Abstract

We give an "excluded minor" and a "structural" characterization of digraphs D that have the property that for every subdigraph H of D, the maximum number of disjoint circuits in H is equal to the minimum cardinality of a subset T of V(H) such that H\T is acyclic.