Small point sets for simply-nested planar graphs

Authors:
Patrizio Angelini;Giuseppe Di Battista;Michael Kaufmann;Tamara Mchedlidze;Vincenzo Roselli;Claudio Squarcella
Affiliations:
Dip. di Informatica e Automazione, Roma Tre University, Italy;Dip. di Informatica e Automazione, Roma Tre University, Italy;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany;Dept. of Math., National Technical University of Athens, Greece;Dip. di Informatica e Automazione, Roma Tre University, Italy;Dip. di Informatica e Automazione, Roma Tre University, Italy
Venue:
GD'11 Proceedings of the 19th international conference on Graph Drawing
Year:
2011

Citing 8
Cited 2

Embedding planar graphs in four pages

Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
A lower bound on the size of universal sets for planar graphs

ACM SIGACT News
Finding Hamiltonian cycles in certain planar graphs

Information Processing Letters
Approximation algorithms for NP-complete problems on planar graphs

Journal of the ACM (JACM)
Embedding planar graphs on the grid

SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On embedding an outer-planar graph in a point set

Computational Geometry: Theory and Applications
A 1.235 lower bound on the number of points needed to draw all n-vertex planar graphs

Information Processing Letters
Minimum-width grid drawings of plane graphs

Computational Geometry: Theory and Applications

h-quasi planar drawings of bounded treewidth graphs in linear area

WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Universal point sets for planar three-trees

WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures

Quantified Score

Hi-index	0.00

Visualization

Abstract

A point set P⊆ℝ2 is universal for a class $\cal G$ if every graph of ${\cal G}$ has a planar straight-line embedding into P. We prove that there exists a $O(n (\frac{\log n}{\log\log n})^2)$ size universal point set for the class of simply-nested n-vertex planar graphs. This is a step towards a full answer for the well-known open problem on the size of the smallest universal point sets for planar graphs [1, 5, 9].