Theory of Computing Systems

, Volume 62, Issue 6, pp 1366–1391 | Cite as

Online Chromatic Number is PSPACE-Complete

  • Martin Böhm
  • Pavel VeselýEmail author
Part of the following topical collections:
  1. Special Issue on Combinatorial Algorithms


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.


PSPACE-completeness Online coloring Online chromatic number 



The authors thank Christian Kudahl and their supervisor Jiří Sgall for useful discussions on the problem.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Computer Science Institute of Charles UniversityPragueCzech Republic

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