Online Chromatic Number is PSPACE-Complete
Martin B\"ohm, Pavel Vesel\'y

TL;DR
This paper proves that determining the online chromatic number of a graph, where vertices arrive sequentially and must be colored immediately, is a PSPACE-complete problem, highlighting its computational complexity.
Contribution
It establishes the PSPACE-completeness of computing the online chromatic number, a significant complexity result in online graph coloring.
Findings
Computing the online chromatic number is PSPACE-complete.
The problem remains hard even with known graph structure.
Implications for online algorithms and complexity theory.
Abstract
In the online graph coloring problem, vertices from a graph G, known in advance, arrive in an online fashion and an algorithm must immediately assign a color to each incoming vertex v so that the revealed graph is properly colored. The exact location of v in the graph G is not known to the algorithm. The online chromatic number of G is the smallest number of colors such that some online algorithm is able to properly color G for any incoming order. We prove that computing the online chromatic number of a graph is PSPACE-complete.
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.
