Universal Point Subsets for Planar Graphs [chapter]

Patrizio Angelini, Carla Binucci, William Evans, Ferran Hurtado, Giuseppe Liotta, Tamara Mchedlidze, Henk Meijer, Yoshio Okamoto
2012 Lecture Notes in Computer Science  
A set S of k points in the plane is a universal point subset for a class G of planar graphs if every graph belonging to G admits a planar straight-line drawing such that k of its vertices are represented by the points of S. In this paper we study the following main problem: For a given class of graphs, what is the maximum k such that there exists a universal point subset of size k? We provide a ⌈ √ n ⌉ lower bound on k for the class of planar graphs with n vertices. In addition, we consider the
more » ... value F (n, G) such that every set of F (n, G) points in general position is a universal subset for all graphs with n vertices belonging to the family G, and we establish upper and lower bounds for F (n, G) for different families of planar graphs, including 4-connected planar graphs and nested-triangles graphs.
doi:10.1007/978-3-642-35261-4_45 fatcat:fuaokaa5obatta2sbwcsgx6m2e