A note on coloring line arrangements

作者：Ackerman Eyal^*; Pach Janos; Pinchasi Rom; Radoicic Rados; Toth Geza

来源：ELECTRONIC JOURNAL OF COMBINATORICS, 2014, 21(2): P2.23.

DOI：10.37236/2660

• Arrangements of lines
• chromatic number
• sparse hypergraphs

We show that the lines of every arrangement of n lines in the plane can be colored with O(root n/log n) colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a circle minus(root/log n) factor. Any further improvement on this bound would also improve the best known lower bound on the following problem of Erdos: estimate the maximum number of points in general position within a set of n points containing no four collinear points.

• 出版日期2014-5-9