Abstract
Although deciding whether the vertices of a planar graph can be colored with three colors is NP-hard, the widely known Grötzsch’s theorem states that every triangle-free planar graph is 3-colorable. We show the first o(n 2) algorithm for 3-coloring vertices of triangle-free planar graphs. The time complexity of the algorithm is \(\mathcal{O}(n\log n)\) .
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A preliminary version of this paper [1] was presented at ESA 2004.
The research has been partially supported by grants from the Polish Ministry of Science and Higher Education, projects 4T11C04425 and N206 005 32/0807. A part of the research was done during the author’s stay at BRICS, Aarhus University, Denmark.
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Kowalik, L. Fast 3-coloring Triangle-Free Planar Graphs. Algorithmica 58, 770–789 (2010). https://doi.org/10.1007/s00453-009-9295-2
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DOI: https://doi.org/10.1007/s00453-009-9295-2