A note on finding long directed cycles above the minimum degree bound in 2-connected digraphs
Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Czyżewska, Jadwiga, Pilipczuk, Marcin
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415345166
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