
TL;DR
This paper corrects a previous claim by showing that an oriented cycle can be 3-colored if and only if its arc imbalance is divisible by three or it lacks three consecutive arcs in the same direction.
Contribution
It provides a precise characterization of 3-colorability for directed cycles, correcting and refining earlier incomplete results.
Findings
3-colorability depends on arc imbalance modulo 3
Cycles without three consecutive same-direction arcs are 3-colorable
The previous condition based solely on arc imbalance is incorrect
Abstract
Sopena in his survey [E. Sopena, The oriented chromatic number of graphs: A short survey, preprint 2013] writes, without any proof, that an oriented cycle can be colored with three colors if and only if , where is the number of forward arcs minus the number of backward arcs in . This is not true. In this paper we show that can be colored with three colors if and only if or does not contain three consecutive arcs going in the same direction.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsDNA and Biological Computing · Protein Degradation and Inhibitors
