A half-integral Erdős-Pósa theorem for directed odd cyclesopen access
- Authors
- Kawarabayashi, Ken-Ichi; Kreutzer, Stephan; Kwon, O-Joung; Xie, Qiqin
- Issue Date
- Jan-2023
- Publisher
- Association for Computing Machinery
- Citation
- Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, v.2023-January, pp.3043 - 3062
- Indexed
- SCOPUS
- Journal Title
- Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
- Volume
- 2023-January
- Start Page
- 3043
- End Page
- 3062
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/191251
- DOI
- 10.1137/1.9781611977554.ch118
- ISSN
- 0000-0000
- Abstract
- We prove that there exists a function f : ℕ → 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 also give a polynomial-time algorithm for fixed k which outputs one of the two outcomes. Using this algorithmic result, we give a polynomial-time algorithm for fixed k to decide whether such k directed odd cycles exist, or there are no k vertex-disjoint directed odd cycles. This extends the half-integral Erdős-Pósa theorem for undirected odd cycles by Reed [Combinatorica 1999] to directed graphs.
- Files in This Item
-
- Appears in
Collections - 서울 자연과학대학 > 서울 수학과 > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/191251)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.