---
title: Strictly convex drawings of planar graphs
url: https://www.emergentmind.com/papers/0507030
type: paper
arxiv_id: '0507030'
arxiv_url: https://arxiv.org/abs/0507030
published: '2005-07-11'
categories:
- cs.CG
- cs.DM
---

# Strictly convex drawings of planar graphs

## Abstract

Every three-connected planar graph with n vertices has a drawing on an O(n^2) x O(n^2) grid in which all faces are strictly convex polygons. These drawings are obtained by perturbing (not strictly) convex drawings on O(n) x O(n) grids. More generally, a strictly convex drawing exists on a grid of size O(W) x O(n^4/W), for any choice of a parameter W in the range n<W<n^2. Tighter bounds are obtained when the faces have fewer sides. In the proof, we derive an explicit lower bound on the number of primitive vectors in a triangle.