有向奇环的半积分Erdős-Pósa定理

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2025-01-07 DOI:10.1016/j.jctb.2024.12.008

Ken-ichi Kawarabayashi , Stephan Kreutzer , O-joung Kwon , Qiqin Xie

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引用次数: 0

摘要

我们证明了存在一个函数f:N→R，使得每个有向图G包含k个有向奇环，其中G的每个顶点最多包含在其中两个有向奇环中，或者是一个最多包含f(k)个顶点满足所有有向奇环的集合。我们给出了一个固定k的多项式时间算法，它输出两个结果中的一个。这将Reed [Combinatorica 1999]关于无向奇环的半积分Erdős-Pósa定理推广到有向图。

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A half-integral Erdős-Pósa theorem for directed odd cycles

We prove that there exists a function

f : N \to R

such that every directed graph G contains either k directed odd cycles where every vertex of G is contained in at most two of them, or a set of at most

f (k)

vertices meeting all directed odd cycles. We give a polynomial-time algorithm for fixed k which outputs one of the two outcomes. This extends the half-integral Erdős-Pósa theorem for undirected odd cycles by Reed [Combinatorica 1999] to directed graphs.

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.