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.
KeywordsPSPACE-completeness Online coloring Online chromatic number
The authors thank Christian Kudahl and their supervisor Jiří Sgall for useful discussions on the problem.
- 3.Böhm, M., Veselý, P.: Online chromatic number is PSPACE-complete. In: Proceedings of 27th international workshop on combinatorial algorithms (IWOCA 2016). LNCS 9843, pp. 16–28 (2016)Google Scholar
- 4.Csernenszky, A., Martin, R.R., Pluhár, A.: On the complexity of Chooser-Picker positional games. arXiv:1605.05430 (2016)
- 5.Dvořák, P., Valla, T.: On the computational complexity and strategies of online Ramsey theory. In: Proceedings of 8th European conference on combinatorics, graph theory and applications (EuroComb 2015), vol. 49, pp. 729–736 (2015)Google Scholar
- 12.Kudahl, C.: On-line graph coloring. Master’s thesis, University of Southern Denmark (2013)Google Scholar