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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.