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On the infinite Lucchesi–Younger conjecture I
Author(s) -
Gollin J. Pascal,
Heuer Karl
Publication year - 2021
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22680
Subject(s) - digraph , conjecture , mathematics , combinatorics , countable set , disjoint sets , discrete mathematics , directed graph , strongly connected component , graph
A dicut in a directed graph is a cut for which all of its edges are directed to a common side of the cut. A famous theorem of Lucchesi and Younger states that in every finite digraph the least size of an edge set meeting every dicut equals the maximum number of disjoint dicuts in that digraph. In this first paper out of a series of two papers, we conjecture a version of this theorem using a more structural description of this min‐max property for finite dicuts in infinite digraphs. We show that this conjecture can be reduced to countable digraphs where the underlying undirected graph is 2‐connected, and we prove several special cases of the conjecture.