Online Chromatic Number is PSPACE-Complete
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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.
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