Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
