Counting Carambolas
Combinatorics
2015-09-22 v2 Discrete Mathematics
Abstract
We give upper and lower bounds on the maximum and minimum number of geometric configurations of various kinds present (as subgraphs) in a triangulation of points in the plane. Configurations of interest include \emph{convex polygons}, \emph{star-shaped polygons} and \emph{monotone paths}. We also consider related problems for \emph{directed} planar straight-line graphs.
Cite
@article{arxiv.1410.1579,
title = {Counting Carambolas},
author = {Adrian Dumitrescu and Maarten Löffler and André Schulz and Csaba D. Tóth},
journal= {arXiv preprint arXiv:1410.1579},
year = {2015}
}
Comments
update reflects journal version, to appear in Graphs and Combinatorics; 18 pages, 13 figures