, Volume 58, Issue 3, pp 770–789 | Cite as

Fast 3-coloring Triangle-Free Planar Graphs

  • Lukasz KowalikEmail author


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 \(\mathcal{O}(n\log n)\) .


Graph algorithms Triangle-free planar graphs Grötzsch’s theorem Coloring Efficient algorithm 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland

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