scholarly journals A Note on Universal Point Sets for Planar Graphs

2020 ◽  
Vol 24 (3) ◽  
pp. 247-267 ◽  
Author(s):  
Manfred Scheucher ◽  
Hendrik Schrezenmaier ◽  
Raphael Steiner
Keyword(s):  
Planar Graphs ◽  
Point Sets ◽  
Universal Point Sets

scholarly journals On Universal Point Sets for Planar Graphs

2015 ◽  
Vol 19 (1) ◽  
pp. 529-547 ◽  
Author(s):  
Jean Cardinal ◽  
Michael Hoffmann ◽  
Vincent Kusters
Keyword(s):  
Planar Graphs ◽  
Point Sets ◽  
Universal Point Sets

scholarly journals Universal Point Sets for Drawing Planar Graphs with Circular Arcs

2014 ◽  
Vol 18 (3) ◽  
pp. 313-324 ◽  
Author(s):  
Patrizio Angelini ◽  
David Eppstein ◽  
Fabrizio Frati ◽  
Michael Kaufmann ◽  
Sylvain Lazard ◽  
...  
Keyword(s):  
Planar Graphs ◽  
Point Sets ◽  
Circular Arcs ◽  
Universal Point Sets

scholarly journals Universal point sets for planar three-trees

2015 ◽  
Vol 30 ◽  
pp. 101-112 ◽  
Author(s):  
Radoslav Fulek ◽  
Csaba D. Tóth
Keyword(s):  
Point Sets ◽  
Universal Point Sets

scholarly journals Counting Triangulations of Planar Point Sets

10.37236/557 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Micha Sharir ◽  
Adam Sheffer
Keyword(s):  
Upper Bound ◽  
Planar Graphs ◽  
Spanning Trees ◽  
Upper Bounds ◽  
Line Graphs ◽  
Point Sets ◽  
Planar Point ◽  
Straight Line ◽  
Point Set ◽  
Spanning Cycles

We study the maximal number of triangulations that a planar set of $n$ points can have, and show that it is at most $30^n$. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous best upper bound of $43^n$ for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing-free) straight-line graphs on a given point set. Specifically, it can be used to derive new upper bounds for the number of planar graphs ($207.84^n$), spanning cycles ($O(68.67^n)$), spanning trees ($O(146.69^n)$), and cycle-free graphs ($O(164.17^n)$).

scholarly journals On Point-Sets That Support Planar Graphs

2012 ◽  
pp. 64-74 ◽  
Author(s):  
Vida Dujmovic ◽  
William Evans ◽  
Sylvain Lazard ◽  
William Lenhart ◽  
Giuseppe Liotta ◽  
...  
Keyword(s):  
Planar Graphs ◽  
Point Sets

scholarly journals Small Point Sets for Simply-Nested Planar Graphs

2012 ◽  
pp. 75-85 ◽  
Author(s):  
Patrizio Angelini ◽  
Giuseppe Di Battista ◽  
Michael Kaufmann ◽  
Tamara Mchedlidze ◽  
Vincenzo Roselli ◽  
...  
Keyword(s):  
Planar Graphs ◽  
Point Sets ◽  
Small Point
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