Online Chromatic Number is PSPACE-Complete
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, since it sees only previously colored neighbors of v. 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.
The authors thank Christian Kudahl and their supervisor Jiří Sgall for useful discussions on the problem.
- 2.Böhm, M., Veselý, P.: Online chromatic number is PSPACE-complete, arXiv preprint (2016). https://arxiv.org/abs/1604.05940
- 4.Gyárfás, A., Kiraly, Z., Lehel, J.: On-line graph coloring and finite basis problems. In: Combinatorics: Paul Erdos is Eighty, vol. 1, pp. 207–214 (1993)Google Scholar
- 9.Kudahl, C.: On-line graph coloring. Master’s thesis, University of Southern Denmark (2013)Google Scholar