A note on finding long directed cycles above the minimum degree bound in 2-connected digraphs
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915372253315072 |
|---|---|
| author | Czyżewska, Jadwiga Pilipczuk, Marcin |
| author_facet | Czyżewska, Jadwiga Pilipczuk, Marcin |
| contents | For a directed graph $G$, let $\mathrm{mindeg}(G)$ be the minimum among in-degrees and out-degrees of all vertices of $G$. It is easy to see that $G$ contains a directed cycle of length at least $\mathrm{mindeg}(G)+1$. In this note, we show that, even if $G$ is $2$-connected, it is NP-hard to check if $G$ contains a cycle of length at least $\mathrm{mindeg}(G)+3$. This is in contrast with recent algorithmic results of Fomin, Golovach, Sagunov, and Simonov [SODA 2022] for analogous questions in undirected graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on finding long directed cycles above the minimum degree bound in 2-connected digraphs Czyżewska, Jadwiga Pilipczuk, Marcin Data Structures and Algorithms For a directed graph $G$, let $\mathrm{mindeg}(G)$ be the minimum among in-degrees and out-degrees of all vertices of $G$. It is easy to see that $G$ contains a directed cycle of length at least $\mathrm{mindeg}(G)+1$. In this note, we show that, even if $G$ is $2$-connected, it is NP-hard to check if $G$ contains a cycle of length at least $\mathrm{mindeg}(G)+3$. This is in contrast with recent algorithmic results of Fomin, Golovach, Sagunov, and Simonov [SODA 2022] for analogous questions in undirected graphs. |
| title | A note on finding long directed cycles above the minimum degree bound in 2-connected digraphs |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2507.03807 |