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A note on coloring line arrangements | Eyal Ackerman
; Rom Pinchasi
; | Date: |
30 Jun 2012 | Abstract: | We show that the lines of every arrangement of $n$ lines in the plane can be
colored with $O(sqrt{n/ log n})$ colors such that no face of the arrangement
is monochromatic. This improves a bound of Bose et al. cite{BCC12} by a
$Theta(sqrt{log n})$ factor. Any further improvement on this bound will
improve the best known lower bound on the following problem of ErdH{o}s:
Estimate the maximum number of points in general position within a set of $n$
points containing no four collinear points. | Source: | arXiv, 1207.0080 | Services: | Forum | Review | PDF | Favorites |
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