1 research outputs found
How many vertex locations can be arbitrarily chosen when drawing planar graphs?
It is proven that every set of distinct points in the plane with
cardinality can be a subset of the
vertices of a crossing-free straight-line drawing of any planar graph with
vertices. It is also proven that if is restricted to be a one-sided convex
point set, its cardinality increases to . The proofs
are constructive and give rise to O(n)-time drawing algorithms. As a part of
our proofs, we show that every maximal planar graph contains a large induced
biconnected outerplanar graphs and a large induced outerpath (an outerplanar
graph whose weak dual is a path)