Geodesic
More Turán-type theorems for triangles in convex point sets
Boris Aronov1 ; Vida Dujmović2 ; Pat Morin3 ; Aurélien Ooms4 ; Luı́s Fernando Schultz Xavier da Silveira3
1New York University
2University of Ottawa
3Carleton University
4Université libre de Bruxelles
The electronic journal of combinatorics, Tome 26 (2019) no. 1
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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.
DOI : 10.37236/7224
Classification : 90C35, 05D99

Boris Aronov  1   ; Vida Dujmović  2   ; Pat Morin  3   ; Aurélien Ooms  4   ; Luı́s Fernando Schultz Xavier da Silveira  3

1 New York University
2 University of Ottawa
3 Carleton University
4 Université libre de Bruxelles 
@article{10_37236_7224,
     author = {Boris Aronov and Vida Dujmovi\'c and Pat Morin and Aur\'elien Ooms and Lu{\i}́s Fernando Schultz Xavier da Silveira},
     title = {More {Tur\'an-type} theorems for triangles in convex point sets},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {1},
     doi = {10.37236/7224},
     zbl = {1409.90212},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7224/}
}
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Boris Aronov; Vida Dujmović; Pat Morin; Aurélien Ooms; Luı́s Fernando Schultz Xavier da Silveira. More Turán-type theorems for triangles in convex point sets. The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/7224

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