Partitions of planar point sets into polygons

Ajit Arvind Diwan; Bodhayan Roy

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arXiv · 1605.05546

Partitions of planar point sets into polygons

Ajit Arvind Diwan·Bodhayan Roy

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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 $2$-factor in the visibility graph of the point set. The characterization for the case where all cycles have length $3$ also translates to finding a $K_3$-factor of the visibility graph of the point set. We show that the generalized problem of finding a $K_k$-factor of the visibility graph of a given point set for $k \geq 5$ is NP-hard.

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Ajit Arvind Diwan, Bodhayan Roy. 2016-05-18. Partitions of planar point sets into polygons. https://arxiv.org/abs/1605.05546

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