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Jochen, Pascal Gollin
이산수학 그룹
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On the infinite Lucchesi–Younger conjecture I

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Title
On the infinite Lucchesi–Younger conjecture I
Author(s)
J. Pascal Gollin; Heuer, Karl
Publication Date
2021-09
Journal
Journal of Graph Theory, v.98, no.1, pp.27 - 48
Publisher
John Wiley and Sons Inc
Abstract
© 2021 The Authors. Journal of Graph Theory published by Wiley Periodicals LLCA 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.
URI
https://pr.ibs.re.kr/handle/8788114/10037
DOI
10.1002/jgt.22680
ISSN
0364-9024
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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