Online Chromatic Number is PSPACE-Complete

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  1. Special Issue on Combinatorial Algorithms

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, 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.

Keywords

PSPACE-completeness Online coloring Online chromatic number 

Notes

Acknowledgments

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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