More turán-type theorems for triangles in convex point sets

Boris Aronov, Vida Dujmović, Pat Morin, Aurélien Ooms, Luís Fernando, Schultz Xavier da Silveira

    Research output: Contribution to journalArticle

    Abstract

    We study the following family of problems: Given a set of n points in convex position, what is the maximum number triangles one can create having these points as vertices while avoiding certain sets of forbidden configurations. As forbidden configurations we consider all 8 ways in which a pair of triangles in such a point set can interact. This leads to 256 extremal Turán-type questions. We give nearly tight (within a log n factor) bounds for 248 of these questions and show that the remaining 8 questions are all asymptotically equivalent to Stein’s longstanding tripod packing problem.

    Original languageEnglish (US)
    Article number#P1.8
    JournalElectronic Journal of Combinatorics
    Volume26
    Issue number1
    StatePublished - Jan 1 2019

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    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Discrete Mathematics and Combinatorics
    • Computational Theory and Mathematics
    • Applied Mathematics

    Cite this

    Aronov, B., Dujmović, V., Morin, P., Ooms, A., Fernando, L., & Silveira, S. X. D. (2019). More turán-type theorems for triangles in convex point sets. Electronic Journal of Combinatorics, 26(1), [#P1.8].