Unimaximal Sequences of Pairs in Rectangle Visibility Drawing

  • Jan Štola
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)


We study the existence of unimaximal subsequences in sequences of pairs of integers, e.g., the subsequences that have exactly one local maximum in each component of the subsequence. We show that every sequence of \(\frac{1}{12}n^2(n^2-1)+1\) pairs has a unimaximal subsequence of length n. We prove that this bound is tight. We apply this result to the problem of the largest complete graph with a 3D rectangle visibility representation and improve the upper bound from 55 to 50.


Complete Graph Previous Lemma Visibility Graph Graph Drawing Minimal Index 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jan Štola
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPragueCzech Republic

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