More Tur\'an-Type Theorems for Triangles in Convex Point Sets

Autor:	Aronov, Boris, Dujmović, Vida, Morin, Pat, Ooms, Aurélien, da Silveira, Luís Fernando Schultz Xavier
Rok vydání:	2017
Předmět:	Mathematics - Combinatorics Computer Science - Computational Geometry Computer Science - Discrete Mathematics
Druh dokumentu:	Working Paper
Popis:	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 Tur\'an-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. Comment: 25 pages, 14 figures, 16 graphics. This version corrects one theorem statement from the original version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1706.10193 Zobrazit plný text záznamu View this record from Arxiv