International Symposium on Mathematical Foundations of Computer Science

MFCS 2015: Mathematical Foundations of Computer Science 2015 pp 407-419 | Cite as

Upper and Lower Bounds on Long Dual Paths in Line Arrangements

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9235)

Abstract

Given a line arrangement \(\mathcal A\) with n lines, we show that there exists a path of length \(n^2/3 - O(n)\) in the dual graph of \(\mathcal A\) formed by its faces. This bound is tight up to lower order terms. For the bicolored version, we describe an example of a line arrangement with 3k blue and 2k red lines with no alternating path longer than 14k. Further, we show that any line arrangement with n lines has a coloring such that it has an alternating path of length \(\varOmega (n^2/ \log n)\). Our results also hold for pseudoline arrangements.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Technische Universität BerlinBerlinGermany
  2. 2.Freie Universität BerlinBerlinGermany

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