Abstract
We show that the maximum number of different square substrings in unrooted labelled trees behaves much differently than in words. A substring in a tree corresponds (as its value) to a simple path. Let \(\textsf{sq}(n)\) be the maximum number of different square substrings in a tree of size n. We show that asymptotically \(\textsf{sq}(n)\) is strictly between linear and quadratic orders, for some constants c 1,c 2 > 0 we obtain:
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Crochemore, M. et al. (2012). The Maximum Number of Squares in a Tree. In: Kärkkäinen, J., Stoye, J. (eds) Combinatorial Pattern Matching. CPM 2012. Lecture Notes in Computer Science, vol 7354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31265-6_3
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DOI: https://doi.org/10.1007/978-3-642-31265-6_3
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