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Covering a supermodular-like function in a mixed hypergraph.

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Title: Covering a supermodular-like function in a mixed hypergraph.
Authors: Gao, Hui1 (AUTHOR) gaoh1118@yeah.net
Source: Discrete Applied Mathematics. May2026, Vol. 385, p72-76. 5p.
Subjects: Matroids, Hypergraphs, Set functions, Directed graphs, Combinatorial optimization, Submodular functions
Abstract: In this paper, we solve a conjecture by Szigeti in [Matroid-rooted packing of arborescences], which characterizes mixed hypergraphs F = (V , E ∪ A) for which there exists an orientation E ⃗ of E such that e E ⃗ ∪ A (P) ≥ ∑ X ∈ P h (X) − b (∪ P) for every subpartition P of V , where h is an integer-valued, intersecting supermodular function on V and b a submodular function on V. As a corollary, another conjecture in the same paper is confirmed, which characterizes mixed hypergraphs admitting a packing of mixed hyperarborescences such that their roots form a basis in a given matroid, each vertex v belongs to exactly k of them and is the root of at least f (v) and at most g (v) of them. [ABSTRACT FROM AUTHOR]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 192194648
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  Data: Covering a supermodular-like function in a mixed hypergraph.
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  Data: In this paper, we solve a conjecture by Szigeti in [Matroid-rooted packing of arborescences], which characterizes mixed hypergraphs F = (V , E ∪ A) for which there exists an orientation E ⃗ of E such that e E ⃗ ∪ A (P) ≥ ∑ X ∈ P h (X) − b (∪ P) for every subpartition P of V , where h is an integer-valued, intersecting supermodular function on V and b a submodular function on V. As a corollary, another conjecture in the same paper is confirmed, which characterizes mixed hypergraphs admitting a packing of mixed hyperarborescences such that their roots form a basis in a given matroid, each vertex v belongs to exactly k of them and is the root of at least f (v) and at most g (v) of them. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.dam.2026.01.023
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 5
        StartPage: 72
    Subjects:
      – SubjectFull: Matroids
        Type: general
      – SubjectFull: Hypergraphs
        Type: general
      – SubjectFull: Set functions
        Type: general
      – SubjectFull: Directed graphs
        Type: general
      – SubjectFull: Combinatorial optimization
        Type: general
      – SubjectFull: Submodular functions
        Type: general
    Titles:
      – TitleFull: Covering a supermodular-like function in a mixed hypergraph.
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            – D: 31
              M: 05
              Text: May2026
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              Y: 2026
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              Value: 385
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            – TitleFull: Discrete Applied Mathematics
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