English

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 nn 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.

Keywords

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

R2 v1 2026-06-22T06:14:36.299Z