超图中树杈填充增广

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-10-09 DOI:10.1016/j.disc.2025.114837

Pierre Hoppenot, Zoltán Szigeti

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引用次数: 0

摘要

我们加深了组合优化的两个经典领域之间的联系：增强和填充树。我们考虑以下类型的问题：添加到有向图上的最小弧数是多少，使得在得到的有向图中存在某种特殊的树形排列？我们用两个问题回答了这个问题：混合超枝的h正则m独立根（f,g）有界（α,β）有限填充和k超枝的h正则（r, r′）有界（α,β）有限填充。我们还解决了后者的无向对应问题，即k根超森林的h正则（r, r′）有边（α,β）有限填充的增广问题。我们的结果提供了大量以往结果的共同概括。

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On arborescence packing augmentation in hypergraphs

We deepen the link between two classic areas of combinatorial optimization: augmentation and packing arborescences. We consider the following type of questions: What is the minimum number of arcs to be added to a digraph so that in the resulting digraph there exists some special kind of packing of arborescences? We answer this question for two problems: h-regular M-independent-rooted

(f, g)

-bounded

(α, β)

-limited packing of mixed hyperarborescences and h-regular

(ℓ, ℓ^{'})

-bordered

(α, β)

-limited packing of k hyperbranchings. We also solve the undirected counterpart of the latter, that is the augmentation problem for h-regular

(ℓ, ℓ^{'})

-bordered

(α, β)

-limited packing of k rooted hyperforests. Our results provide a common generalization of a great number of previous results.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.