English

Partitions of planar point sets into polygons

Computational Geometry 2016-05-19 v1

Abstract

In this paper, we characterize planar point sets that can be partitioned into disjoint polygons of arbitrarily specified sizes. We provide an algorithm to construct such a partition, if it exists, in polynomial time. We show that this problem is equivalent to finding a specified 22-factor in the visibility graph of the point set. The characterization for the case where all cycles have length 33 also translates to finding a K3K_3-factor of the visibility graph of the point set. We show that the generalized problem of finding a KkK_k-factor of the visibility graph of a given point set for k5k \geq 5 is NP-hard.

Keywords

Cite

@article{arxiv.1605.05546,
  title  = {Partitions of planar point sets into polygons},
  author = {Ajit Arvind Diwan and Bodhayan Roy},
  journal= {arXiv preprint arXiv:1605.05546},
  year   = {2016}
}
R2 v1 2026-06-22T14:03:41.337Z