Abstract
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.
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Štola, J. (2009). Unimaximal Sequences of Pairs in Rectangle Visibility Drawing. In: Tollis, I.G., Patrignani, M. (eds) Graph Drawing. GD 2008. Lecture Notes in Computer Science, vol 5417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00219-9_7
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DOI: https://doi.org/10.1007/978-3-642-00219-9_7
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