Abstract
We show the first o(n 2) algorithm for coloring vertices of triangle-free planar graphs using three colors. The time complexity of the algorithm is \(\mathcal{O}\) (n log n). Our approach can be also used to design \(\mathcal{O}\)(n polylog n)-time algorithms for two other similar coloring problems.
A remarkable ingredient of our algorithm is the data structure processing short path queries introduced recently in [9]. In this paper we show how to adapt it to the fully dynamic environment where edge insertions and deletions are allowed.
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Kowalik, Ł. (2004). Fast 3-Coloring Triangle-Free Planar Graphs. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_40
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DOI: https://doi.org/10.1007/978-3-540-30140-0_40
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