Abstract
We consider proper online colorings of hypergraphs defined by geometric regions. We prove that there is an online coloring method that colors N intervals of the real line using Θ(logN/k) colors such that for every point p, contained in at least k intervals, not all the intervals containing p have the same color. We also prove the corresponding result about online coloring quadrants in the plane that are parallel to a given fixed quadrant. These results contrast to recent results of the first and third author showing that in the quasi-online setting 12 colors are enough to color quadrants (independent of N and k). We also consider coloring intervals in the quasi-online setting. In all cases we present efficient coloring algorithms as well.
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Keszegh, B., Lemons, N., Pálvölgyi, D. (2013). Online and Quasi-online Colorings of Wedges and Intervals. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds) SOFSEM 2013: Theory and Practice of Computer Science. SOFSEM 2013. Lecture Notes in Computer Science, vol 7741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35843-2_26
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DOI: https://doi.org/10.1007/978-3-642-35843-2_26
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