More TuránType Theorems for Triangles in Convex Point Sets
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 Turántype 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2017
 arXiv:
 arXiv:1706.10193
 Bibcode:
 2017arXiv170610193A
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Computational Geometry;
 Computer Science  Discrete Mathematics
 EPrint:
 25 pages, 14 figures, 16 graphics. This version corrects one theorem statement from the original version