In this paper, we design the first polynomial time approximation schemes for the Set Cover
and Dominating Set problems when the underlying sets are non-piercing regions (which …

Consider the following problem: Given a planar graph $ G $, what is the maximum number $
p $ such that $ G $ has a planar straight-line drawing with $ p $ collinear vertices? This …

A subset $ S $ of vertices in a planar graph $ G $ is a free set if, for every set $ P $ of $| S| $
points in the plane, there exists a straight-line crossing-free drawing of $ G $ in which …

In this note we show how techniques developed for untangling planar graphs by Bose et
al.[Discrete & Computational Geometry 42 (4): 570-585 (2009)] and Goaoc et al.[Discrete & …

We show that if a planar graph G has a plane straight-line drawing in which a subset S of its
vertices are collinear, then for any set of points, X, in the plane with| X|=| S|, there is a plane …

In this paper we show how techniques developed for untangling planar graphs by Bose et
al.[Discrete & Computational Geometry 42 (4): 570–585 (2009)] and Goaoc et al.[Discrete & …

Given a planar graph G, what is the maximum number of collinear vertices in a planar
straight-line drawing of G? This problem resides at the core of several graph drawing …

A point set S ⊆ R^ 2 S⊆ R 2 is universal for a class\mathcal GG of planar graphs if every
graph of GG has a planar straight-line embedding on S S. It is well-known that the integer …

Given a sextuple of distinct points A, B, C, D, E, F on a conic, arranged into an array\big,
ABCFED, Pascal's theorem says that the points AE ∩ BF, BD ∩ CE, AD ∩ CF AE∩ BF …

We show that, if an n-vertex triangulation G of maximum degree Δ has a dual that contains a
cycle of length ℓ, then G has a non-crossing straight-line drawing in which some set, called a …